text:
## The Martian

 Author : Andy Weir Publisher : Ballantine Books Total Pages : 480 Release : 2021-03-30 ISBN 10 : 9780593357132 ISBN 13 : 0593357132 Language : EN, FR, DE, ES & NL

The Martian Book Description:

#1 NEW YORK TIMES BESTSELLER * "Brilliant . . . a celebration of human ingenuity [and] the purest example of real-science sci-fi for many years . . . utterly compelling."--The Wall Street Journal The inspiration for the major motion picture Six days ago, astronaut Mark Watney became one of the first people to walk on Mars. Now, he's sure he'll be the first person to die there. After a dust storm nearly kills him and forces his crew to evacuate while thinking him dead, Mark finds himself stranded and completely alone with no way to even signal Earth that he's alive--and even if he could get word out, his supplies would be gone long before a rescue could arrive. Chances are, though, he won't have time to starve to death. The damaged machinery, unforgiving environment, or plain-old "human error" are much more likely to kill him first. But Mark isn't ready to give up yet. Drawing on his ingenuity, his engineering skills--and a relentless, dogged refusal to quit--he steadfastly confronts one seemingly insurmountable obstacle after the next. Will his resourcefulness be enough to overcome the impossible odds against him? NAMED ONE OF PASTE'S BEST NOVELS OF THE DECADE "A hugely entertaining novel [that] reads like a rocket ship afire . . . Weir has fashioned in Mark Watney one of the most appealing, funny, and resourceful characters in recent fiction."--Chicago Tribune "As gripping as they come . . . You'll be rooting for Watney the whole way, groaning at every setback and laughing at his pitchblack humor. Utterly nail-biting and memorable."--Financial Times

## The Martian Tales

 Author : Rigby Publisher : Rigby Total Pages : 112 Release : 2001-11-16 ISBN 10 : 0757820336 ISBN 13 : 9780757820335 Language : EN, FR, DE, ES & NL

The Martian Tales Book Description:

Life has just turned upside down for Sanders A. Parker. His parents are talking about separating. He is being forced to spend the summer with a grandfather he hardly knows. And he has suddenly realized that he isn't an ordinary kid at all. He can't be--not with all that's going on. He must be a martian--sent to Earth to report on the terrible things that can happen to unsuspecting kids.

## The Martian Visitors

 Author : Howling Wolf Publisher : Total Pages : 239 Release : 1999 ISBN 10 : UOM:39015053116763 ISBN 13 : Language : EN, FR, DE, ES & NL

The Martian Visitors Book Description:

## Ray Bradbury s The Martian Chronicles

 Author : Walter James Miller Publisher : Total Pages : 140 Release : 1998 ISBN 10 : 0760710880 ISBN 13 : 9780760710883 Language : EN, FR, DE, ES & NL

Ray Bradbury s The Martian Chronicles Book Description:

## The Martian Named Smith

 Author : William H. Patterson Publisher : Total Pages : 209 Release : 2001 ISBN 10 : UCSC:32106019041141 ISBN 13 : Language : EN, FR, DE, ES & NL

The Martian Named Smith Book Description:

## Telescopically derived Constraints on the Composition and Thermophysical Properties of the Martian Surface

 Author : Jeffrey Edward Moersch Publisher : Total Pages : 400 Release : 1998 ISBN 10 : CORNELL:31924083616254 ISBN 13 : Language : EN, FR, DE, ES & NL

Telescopically derived Constraints on the Composition and Thermophysical Properties of the Martian Surface Book Description:

Using the SpectroCam-10 instrument on the Hale 200${\sp\prime}{\sp\prime}$ telecope at Palomar observatory, I have obtained an extensive set of images and spectra of Mars in the 7.5-13-$\mu$m region over the course of three successive oppositions. The data have been used to study two basic classes of scientific problems relating to the surface of Mars: the determination of the present-day thermophysical properties of the surface, and the search for spectral emissivity variations indicative of surface mineralogical composition. The results of these analyses are summarized as follows: (1) A time-sequence of thermal emission images taken over the course of one martian day shows that the present-day thermal inertia of the Cerberus region of Mars has changed since the late 1970's. Visible and near-infrared wavelength observations suggest that this change is the result of dust deposition. Modeling of the Palomar thermal IR data shows that the change in thermal inertia may be accounted for with a 2-4 mm mantle of dust, which implies a deposition rate consistent with the highest rates determined using other techniques. A deposition rate of 400 $\mu$m yr$\sp{-1}$ is probably representative of the highest rates occurring on a regional scale on Mars today. (2) A broad spectral feature at 9.2 $\mu$m has been identified in the Acidalia region of Mars. The persistence of this feature over time indicates that it is caused by spectral emissivity variations in surface materials, and not by atmospheric dust absorption. The spectral feature is interpreted to be indicative of a silicate mineralogy on the surface. Its spectral shape is consistent with the laboratory-measured emissivity spectrum of a glassy basalt sample. (3) A global spectral map shows that Acidalia. is not the only region on the planet that displays thermal IR spectral features. Other areas of the planet, concentrated in the northern latitudes, display spectral features similar to Acidalia. There are also regions that display spectral features distinctly different from Acidalia, indicating that the surface of Mars is not mineralogically homogeneous. Areas showing spectral features are spatially well correlated with predictions of a rock abundance model that is based on thermophysical properties.

## Temperature and Composition of the Martian Atmosphere

 Author : Richard Willis Stewart Publisher : Total Pages : 290 Release : 1967 ISBN 10 : NASA:31769000591829 ISBN 13 : Language : EN, FR, DE, ES & NL

Temperature and Composition of the Martian Atmosphere Book Description:

## Exploring an Impact Origin for the Martian Crustal Dichotomy

 Author : Shawn D. Hart Publisher : Total Pages : 146 Release : 2007 ISBN 10 : UCAL:X77875 ISBN 13 : Language : EN, FR, DE, ES & NL

Exploring an Impact Origin for the Martian Crustal Dichotomy Book Description:

## Investigation of solar energy deposited as heat in the martian upper atmosphere

 Author : Robert E. Johnson Publisher : Total Pages : Release : 1979 ISBN 10 : UVA:X004211540 ISBN 13 : Language : EN, FR, DE, ES & NL

Investigation of solar energy deposited as heat in the martian upper atmosphere Book Description:

## Far infrared Spectroscopy of CO2 Clathrate Hydrate with Applications to the Martian Northern Polar Region

 Author : Joseph Carl Landry Publisher : Total Pages : Release : 1995 ISBN 10 : UOM:39015034421795 ISBN 13 : Language : EN, FR, DE, ES & NL

Far infrared Spectroscopy of CO2 Clathrate Hydrate with Applications to the Martian Northern Polar Region Book Description:


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# Does the Electric Field Instantaneously vanish during an Electron Capture?

When an Electron Capture occurs a Neutron and a Neutrino are formed. Prior to this process due to the presence of the proton and electron an electric field must've existed however as soon as this process happens which is almost instantaneous i believe the electric field must vanish right? So what happens does this change propagate at the speed of light i.e. say somewhere 1 light year away the change will be felt after 1 year? Also what happens to the energy (if any) which was stored in the electric field does it go to the Neutron and Neutrino?

Electrons and electron capture belong to particle physics analysis, i.e. one should look at the feynman diagrams for electron capture.

To start with, there is charge conservation at each vertex.Quarks are charged and take the balance: for a proton to turn into a neutron an up quark absorbs a charge of -1 and becomes a down quark. (The particles indicated in the arrows towards a vertex can be read as antiparticles going away from the pointed vertex).

So as far as charge conservation goes the absorption of a virtual $$W^-$$ is what changes the up quark to a down quark. The charge of the incoming electron is transferred by the $$W^-$$ .

i believe the electric field must vanish right

At the particle level there are no electric fields carrying energy. The energy is carried by the particles participating and conservation of energy is a law. The charge carried by particles and there is conservation of charge.

So what happens does this change propagate at the speed of light i.e. say somewhere 1 light year away the change will be felt after 1 year?

At the particle level, as there are no photons in the interaction there is no electromagnetic energy going away from the interaction. There are the neutrinos that carry energy away, and in principle if one had an experiment with accumulated data of electron capture and one had very good neutrino detectors, yes they would be seen in the cosmos. Because of the weak interaction being so weak, it is a science fiction scenario.

Also what happens to the energy (if any) which was stored in the electric field does it go to the Neutron and Neutrino?

At this level of analysis there are no electric fields . The energy of the interaction is shared between the elementary particles involved, according to the boundary conditions of the nucleus involved also.

• The 2 answers deal at different levels of analysis. Is there an objective way to choose a better explanation? Oct 28 '20 at 16:38
• Any proton has an extended electric field around it; so does an electron. To say "at the particle level, there are no electric fields" amounts to saying "the description I am offering here does not account for all the physics; in particular, it does not account for the aspect of the physics that you asked about". Oct 28 '20 at 18:43
• @AndrewSteane The electric field is a classical electrodynamic variable., and there is mathematical continuity in the overlap region between classical and quantum, but it is not useful to mix up frames. I am discussing the quantum mechanical particle frame. see how complicated it is to mix the frames physics.stackexchange.com/questions/214035/… Oct 28 '20 at 20:18
• @FoundABetterName It is not difference in levels, it is a difference in frames. My answer is in the quantum frame of particles, the other answer is in the classical frame.There is mathematical continuity between the frames, but one should not mix them. electron capture is a quantum mechanical interaction. Oct 28 '20 at 20:23

Nothing happens instantaneously. Nuclear processes tend to happen on a faster time scale than chemical & other electronic processes, because of the smaller distances & larger energies involved in nuclear processes.

Electron capture (EC) is a form of weak interaction (which I describe in this answer). Weak processes tend to be somewhat slower than processes governed by the strong nuclear interaction (which binds quarks together, and indirectly binds nucleons together).

In normal matter, the number of electrons equals the number of protons, and since they have the same electric charge normal matter is electrically neutral: there's no appreciable electric field unless you're really close to an atom because the field contributions from the protons & electrons balance each other.

When electron capture occurs, the changes to the electromagnetic field propagate at the speed of light, as usual, but those changes are rather small. Bear in mind that any atom that undergoes EC has multiple protons & electrons, and losing 1 pair doesn't affect the total energy by very much, but it does change the shape of the electrical field, so there are changes in the nucleus as well as in the atom's electronic structure. And of course that electronic structure determines the chemical properties of the atom, as well as most of its physical properties apart from its mass (eg, colour, melting point).

An electron and proton are oppositely charged and together form a dipole, which from a distance looks neutral. As the particles get closer together, the dipole formed gets weaker, until it reaches zero when they merge. The process is not instantaneous.

The change in field propagates at the speed of light. Opposite charges attract, so as the particles approach one another the field does work on them both, accelerating them, extracting energy from the electric field and transfering it into kinetic energy of the converging particles.

In an elastic collision, the electron would whizz round the proton and fly off, like a comet round the sun. But if it comes close enough for the weak interaction to produce a W boson that can hop the gap, the charge goes with the W into the proton, and the remainder of the kinetic energy flies off with the chargeless electron that is now a neutrino. Since a neutron is slightly heavier than a proton, the W must carry a little of the electron's kinetic energy and leave it as the neutron's increased rest mass.

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# Doubt from Properties of triangles

In triangle ABC, Incentre and circum center are reflections of each other in side BC. Measure angle BAC is

Note that OI is perpendicular to BC since I,B are images of each other across BC. Hence OI bisects BC. It is now easy to see that \triangle ABC is isosceles. So that \angle B = 90^{\circ} -\dfrac{A}{2}

We have \angle OBC = \angle IBC = \dfrac{B}{2}=45^{\circ} -\dfrac{A}{4}

Using properties of circles, \angle BOI = 180^{\circ}-A

Now we have that \angle BOI + \angle OBC = 90^{\circ} so that \angle A = 168^{\circ}

1 Like

Correction: \angle A =108^{\circ}

1 Like


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# Line integral question

1. Jul 26, 2005

### asdf1

Calculate the line integral of the function v=(y的平方, 2x(y+1), 0) from the
point a=(1,0,0) to the point b=(2,2,0)
The correct Ans: 11

However, when I was calculuating the problem,
I supposed(is that the right word?) to make the parameter equations,

x=1+t
y=1+t
z=0
where 0<t<1
but when I integrated the function, the answer is 6.

2. Jul 26, 2005

### mantito

i don't know why, but i see your function as some chinese characters, can you retype it in some other way:).

3. Jul 26, 2005

### TD

I'd say

$$\left\{ \begin{array}{l} x = t \\ y = 2t - 2 \\ z = 0 \\ \end{array} \right$$

or

$$\left\{ \begin{array}{l} x = t + 1 \\ y = 2t \\ z = 0 \\ \end{array} \right$$

4. Jul 26, 2005

### HallsofIvy

Staff Emeritus
when t= 0, your parametrization gives (1, 1, 0), there is no value of t that gives (1, 0, 0).

5. Jul 27, 2005

### asdf1

sorry, i mistyped~
a=(1,0,0)


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# Help in understanding this. Is this just an empirical observation on climate sensitivity?

I was reading this on realclimate.org.

My question on the below is this. Physics can tell you the radiative forcing of CO2, which is $$\small\mathsf{5.35ln(Cnew/Cpreindustrial)}$$. This tells you how much radiative forcing to expect for an increase of CO2 (=$$\small\mathsf{C_{new})}$$ over pre-industrial levels (C preindustrial, usually 280 ppm). This formula provides an unambiguous answer of radiative forcing.

But... there is a question that then arises about what warming is associated with this particular level of radiative forcing. This appears to be an empirical matter, looking at past fluctuations of CO2 and associated temperatures. This is the climate sensitivity. There are lots of studies on this, with a now-accepted range of 1.5-4.5 °C. But the reason there is some disagreement about this is that it is an empirical question, not so much a physics one, right?

Here's the realclimate piece:

Blockquote

As the name suggests, climate sensitivity is an estimate of how sensitive the climate is to an increase in a radiative forcing. The climate sensitivity value tells us how much the planet will warm or cool in response to a given radiative forcing change. As you might guess, the temperature change is proportional to the change in the amount of energy reaching the Earth's surface (the radiative forcing), and the climate sensitivity is the coefficient of proportionality:

dT = λ*dF

Where 'dT' is the change in the Earth's average surface temperature, 'λ' is the climate sensitivity, usually with units in Kelvin or degrees Celsius per Watts per square meter (°C/[W/m2]), and 'dF' is the radiative forcing.

So now to calculate the change in temperature, we just need to know the climate sensitivity. Studies have given a possible range of values of 2-4.5 °C warming for a doubling of CO2 (IPCC 2007). Using these values it's a simple task to put the climate sensitivity into the units we need, using the formulas above:

λ = dT/dF = dT/(5.35 * ln[2])= [2 to 4.5 °C]/3.7 = 0.54 to 1.2 °C/(W/m2)

Using this range of possible climate sensitivity values, we can plug λ into the formulas above and calculate the expected temperature change. The atmospheric CO2 concentration as of 2010 is about 390 ppmv. This gives us the value for 'C', and for 'C0' we'll use the pre-industrial value of 280 ppmv.

dT = λ*dF = λ * 5.35 * ln(390/280) = 1.8 * λ

Plugging in our possible climate sensitivity values, this gives us an expected surface temperature change of about 1–2.2 °C of global warming, with a most likely value of 1.4 °C. However, this tells us the equilibrium temperature. In reality it takes a long time to heat up the oceans due to their thermal inertia. For this reason there is currently a planetary energy imbalance, and the surface has only warmed about 0.8 °C. In other words, even if we were to immediately stop adding CO2 to the atmosphere, the planet would warm another ~0.6 °C until it reached this new equilibrium state (confirmed by Hansen 2005). This is referred to as the 'warming in the pipeline'.


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# TensorNodes¶

TensorNodes allow parts of a model to be defined using TensorFlow and smoothly integrated with the rest of a Nengo model. TensorNodes work very similarly to a regular Node, except instead of executing arbitrary Python code they execute arbitrary TensorFlow code.

tensor_layer() is a utility function for constructing TensorNodes, designed to mimic the layer-based model construction style of many deep learning packages.

## API¶

class nengo_dl.tensor_node.TensorNode(tensor_func, size_in=Default, size_out=Default, label=Default)[source]

Inserts TensorFlow code into a Nengo model. A TensorNode operates in much the same way as a Node, except its inputs and outputs are defined using TensorFlow operations.

The TensorFlow code is defined in a function or callable class (tensor_func). This function accepts the current simulation time as input, or the current simulation time and a Tensor x if node.size_in > 0. x will have shape (sim.minibatch_size, node.size_in), and the function should return a Tensor with shape (sim.minibatch_size, node.size_out). node.size_out will be inferred by calling the function once and checking the output, if it isn’t set when the Node is created.

If tensor_func has a pre_build attribute, that function will be called once when the model is constructed. This can be used to compute any constant values or set up variables – things that don’t need to execute every simulation timestep.

Parameters: tensor_func : callable a function that maps node inputs to outputs size_in : int, optional (Default: 0) the number of elements in the input vector size_out : int, optional (Default: None) the number of elements in the output vector (if None, value will be inferred by calling tensor_func) label : str, optional (Default: None) a name for the node, used for debugging and visualization
nengo_dl.tensor_node.tensor_layer(input, layer_func, shape_in=None, synapse=None, transform=1, return_conn=False, **layer_args)[source]

A utility function to construct TensorNodes that apply some function to their input (analogous to the tf.layers syntax).

Parameters: input : nengo.base.NengoObject object providing input to the layer layer_func : callable or NeuronType a function that takes the value from input (represented as a tf.Tensor) and maps it to some output value. or a Nengo neuron type, defining a nonlinearity that will be applied to input shape_in : tuple of int, optional if not None, reshape the input to the given shape synapse : float or Synapse, optional synapse to apply on connection from input to this layer transform : ndarray, optional transform matrix to apply on connection from input to this layer return_conn : bool, optional if True, also return the connection linking this layer to input layer_args : dict, optional these arguments will be passed to layer_func if it is callable, or Ensemble if layer_func is a NeuronType :class:.TensorNode or :class:~nengo:nengo.ensemble.Neurons a TensorNode that implements the given layer function (if layer_func was a callable), or a Neuron object with the given neuron type, connected to input


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# How do I use the existence of an array member as an 'If' condition?

I have an oddly shaped array (it is 100 by 100 by {1 or 3}, with the 1 or 3 being essentially random). I want to run a 'Do' loop on the first 2 dimensions of the array, but I only want to do the thing in the loop when I am at a member with three members in the last dimension. Is there a way to do this? I tried playing with things like If[Array[[i]][[j]][[3]]!=Null,t,f], but to no avail. At the end of the day, what I want is a way to write the following in Mathematica's language:

• If Array[[i]][[j]][[3]] exists, then do expr

• In you If expression test on Length or Dimension. – m_goldberg Aug 15 '17 at 18:59

Clear[f, fakef]
fakeData = Array[Range[RandomChoice[{1, 3}]] &, {10, 10}];
fakef = If[1 == Length[#], #, {Last[#]}] &;
Map[fakef, fakeData, {2}]

Since your question mentions a Do loop over your matrix, (not a Table or Map), I'll first assume you're not building a new matrix, you don't care at all about your single-element data, but you actually really care about the positions of the 3-element-stuff within your structure as well as the 3-element-stuff.

If you don't care about the positions and you're just looking to make a new matrix with your 3-element stuff modified, then as Alan says you can just Map your function at level {2} over your data with a conditional.

First I'll make some stuff;

stuff =  Table[
If[RandomReal[{0, 1}] < .01, {a[i, j], b[i, j], c[i, j]}, d], {i,
1, 100}, {j, 1, 100}];

If you really care about the positions in your matrix, i.e. you want to do something to the 3-element stuff, and you need to know where it came from, but you don't need to make a new matrix:

locationsOfLength3 =
Select[Position[stuff, x_ /; Length[x] === 3], Length[#] === 2 &];

Do[ somethingWithStuff[ stuff[[p[[1]], p[[2]]]] , p ],
{p,locationsOfLength3}]

Note: I'm passing the location to my function as well as what was in stuff at that location. If you don't need the location, and don't need a matrix, you can ignore that bit.

If you need a matrix, but your function somethingWithStuff also needs to know where in your matrix the 3-element-stuff came from, you can do it with MapIndexed:

 newMatrix=MapIndexed[  If[Length[#] === 1, #,
somethingWithStuff[#, #2]] &, stuff, {2}];


text:
## Computation of exponential integrals.(English)Zbl 0436.65006

### MSC:

 65D20 Computation of special functions and constants, construction of tables 33C05 Classical hypergeometric functions, $${}_2F_1$$ 33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)

Zbl 0436.65007
Full Text:


text:
## Reich, Simeon

Compute Distance To:
 Author ID: reich.simeon Published as: Reich, Simeon; Reich, S. Homepage: http://www.math.technion.ac.il/Site/computing/services/staff-card.php?id=681 External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 541 Publications since 1968, including 4 Books 21 Contributions as Editor Reviewing Activity: 102 Reviews Biographic References: 3 Publications Co-Authors: 158 Co-Authors with 465 Joint Publications 3,568 Co-Co-Authors
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### Co-Authors

 94 single-authored 171 Zaslavski, Alexander Yakovlevich 61 Shoikhet, David 35 Kuczumow, Tadeusz 20 Elin, Mark 18 Aizicovici, Sergiu 17 Kopecká, Eva 16 Budzyńska, Monika 15 Censor, Yair 15 Zalas, Rafał 14 Sabach, Shoham 13 Butnariu, Dan 13 Khatskevich, Viktor Anatol’evich 13 Pustylnik, Evgeniy 12 Gibali, Aviv 12 Trương Minh Tuyên 11 Kaczor, Wiesława J. 10 Levenshtein, Marina 9 Reem, Daniel 8 Shafrir, Itai 7 Agranovsky, Mark L. 7 Bruck, Ronald E. jun. 7 Karp, Lavi 7 Rosen, I. Gary 7 Zalcman, Lawrence Allen 6 Ackleh, Azmy S. 6 Aleyner, Arkady 6 Bargetz, Christian 6 Ben-Artzi, Matania 6 Dye, John Michael 6 Weinstein, Gilbert 5 Bartz, Sedi 5 Galloway, Greg 5 Garcia-Falset, Jesús 4 Alber, Yakov I. 4 Banks, Harvey Thomas 4 Cegielski, Andrzej 4 Gabour, Manal 4 Khavinson, Dmitry S. 4 Martín-Márquez, Victoria 4 Stachura, Adam 4 Yacobzon, Fiana 3 Arav, Marina 3 Barshad, Kay 3 Bauschke, Heinz H. 3 Borwein, Jonathan Michael 3 Calvert, Bruce D. 3 de Pierro, Alvaro Rodolfo 3 Demetriou, Michael A. 3 Dương Việt Thông 3 Ha, Mai Thi Ngoc 3 Ioffe, Alexander Davidovich 3 Israel, Maximiano M. jun. 3 Khamsi, Mohamed Amine 3 Kolobov, Victor I. 3 Poffald, Esteban I. 3 Salinas, Zuly 3 Schmidt, Małgorzata 3 Xu, Hong-Kun 2 Aharonov, Dov 2 Alpay, Daniel Aron 2 Baillon, Jean-Bernard 2 Boulos, Wissam 2 Bregman, Lev M. 2 Cholamjiak, Prasit 2 De Blasi, Francesco Saverio 2 Donchev, Tzanko Donchev 2 Dung, Vu Tien 2 Dye, J. 2 Dymond, Michael 2 Farkhi, Elza M. 2 Goebel, Kazimierz 2 Goldvard, Alexander 2 Grzesik, Aleksandra 2 Harris, Lawrence A. 2 Hulbert, Douglas S. 2 Kapeluszny, Jarosław 2 Kirk, William Arthur 2 Lin, Pei-Kee 2 Plant, Andrew T. 2 Shemen, Lital 2 Walczyk, Mariola 2 Wang, Shawn Xianfu 1 Aguirre Salazar, Lorena 1 Aĭzenberg, Lev Abramovich 1 Ariza-Ruiz, David 1 Bačák, Miroslav 1 Bénéteau, Catherine 1 Bonk, Mario 1 Bracci, Filippo 1 Bshouty, Daoud H. 1 Byrne, Charles L. 1 Chen, Yuqing 1 Combettes, Patrick L. 1 Cotta, Carlos C. 1 Dang Van Hieu 1 Dijksma, Aad 1 Dong, Qiaoli 1 Fan, Ky 1 Ferdinand, Robert R. 1 Goryainov, Viktor V. ...and 59 more Co-Authors
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### Serials

 46 Journal of Nonlinear and Convex Analysis 34 Journal of Mathematical Analysis and Applications 20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 19 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 15 Numerical Functional Analysis and Optimization 14 Journal of Fixed Point Theory and Applications 13 Optimization 13 Nonlinear Analysis. Theory, Methods & Applications 11 Contemporary Mathematics 10 Numerical Algorithms 10 Fixed Point Theory 9 Abstract and Applied Analysis 9 Fixed Point Theory and Applications 8 American Mathematical Monthly 8 JP Journal of Fixed Point Theory and Applications 7 Proceedings of the American Mathematical Society 7 Journal of Convex Analysis 6 Journal of Approximation Theory 6 Taiwanese Journal of Mathematics 5 Journal of Functional Analysis 5 Journal of Optimization Theory and Applications 5 Proceedings of the Japan Academy. Series A 5 SIAM Journal on Optimization 5 Electronic Journal of Differential Equations (EJDE) 5 Set-Valued and Variational Analysis 5 Linear and Nonlinear Analysis 4 Houston Journal of Mathematics 4 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 4 Mathematica Japonica 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Panamerican Mathematical Journal 4 Topological Methods in Nonlinear Analysis 4 Communications on Applied Nonlinear Analysis 4 Pure and Applied Functional Analysis 4 Journal of Nonlinear and Variational Analysis 3 Israel Journal of Mathematics 3 Mathematics Magazine 3 Commentationes Mathematicae Universitatis Carolinae 3 Integral Equations and Operator Theory 3 Zeitschrift für Analysis und ihre Anwendungen 3 Dynamic Systems and Applications 3 Journal of Applied Analysis 3 Communications in Applied Analysis 3 Nonlinear Analysis Forum 3 Computational Methods and Function Theory 3 Carpathian Journal of Mathematics 3 Communications in Mathematical Analysis 3 3 Analysis and Mathematical Physics 2 Applicable Analysis 2 Bulletin of the Australian Mathematical Society 2 Journal d’Analyse Mathématique 2 Revue Roumaine de Mathématiques Pures et Appliquées 2 Studia Mathematica 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Bulletin of the Calcutta Mathematical Society 2 Canadian Mathematical Bulletin 2 Colloquium Mathematicum 2 Kybernetika 2 Mathematische Nachrichten 2 SIAM Journal on Control and Optimization 2 Transactions of the American Mathematical Society 2 Comptes Rendus Mathématiques de l’Académie des Sciences 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 The Journal of Analysis 2 Discrete and Continuous Dynamical Systems 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Mathematical Proceedings of the Royal Irish Academy 2 Nonlinear Functional Analysis and Applications 2 International Journal of Pure and Applied Mathematics 2 Bollettino della Unione Matematica Italiana. Series IV 2 Chapman & Hall/CRC Research Notes in Mathematics 2 Complex Analysis and Operator Theory 2 Journal of Mathematics and Applications 2 Journal of Nonlinear Analysis and Optimization: Theory & Applications 1 Inverse Problems 1 Journal of Mathematical and Physical Sciences 1 Linear and Multilinear Algebra 1 The Mathematical Gazette 1 Mathematical Methods in the Applied Sciences 1 Acta Scientiarum Mathematicarum 1 Advances in Mathematics 1 Applied Mathematics and Optimization 1 Archiv der Mathematik 1 Commentarii Mathematici Universitatis Sancti Pauli 1 Dissertationes Mathematicae 1 Indian Journal of Mathematics 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Mathematics of Operations Research 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Complex Variables. Theory and Application 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Differential and Integral Equations 1 Journal of Global Optimization ...and 30 more Serials
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 430 Operator theory (47-XX) 142 General topology (54-XX) 125 Functional analysis (46-XX) 78 Operations research, mathematical programming (90-XX) 66 Calculus of variations and optimal control; optimization (49-XX) 61 Numerical analysis (65-XX) 33 Approximations and expansions (41-XX) 32 Ordinary differential equations (34-XX) 31 Several complex variables and analytic spaces (32-XX) 26 Dynamical systems and ergodic theory (37-XX) 25 Functions of a complex variable (30-XX) 21 Global analysis, analysis on manifolds (58-XX) 20 General and overarching topics; collections (00-XX) 20 Convex and discrete geometry (52-XX) 18 Partial differential equations (35-XX) 11 Real functions (26-XX) 9 Systems theory; control (93-XX) 7 Difference and functional equations (39-XX) 7 Integral equations (45-XX) 5 Geometry (51-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Differential geometry (53-XX) 3 Probability theory and stochastic processes (60-XX) 2 Group theory and generalizations (20-XX) 2 Sequences, series, summability (40-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 2 Biology and other natural sciences (92-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX)

### Citations contained in zbMATH Open

415 Publications have been cited 10,024 times in 4,345 Documents Cited by Year
Uniform convexity, hyperbolic geometry, and nonexpansive mappings. Zbl 0537.46001
Goebel, Kazimierz; Reich, Simeon
1984
Strong convergence theorems for resolvents of accretive operators in Banach spaces. Zbl 0437.47047
Reich, Simeon
1980
Weak convergence theorems for nonexpansive mappings in Banach spaces. Zbl 0423.47026
Reich, Simeon
1979
Algorithms for the split variational inequality problem. Zbl 1239.65041
Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
The subgradient extragradient method for solving variational inequalities in Hilbert space. Zbl 1229.58018
Censor, Y.; Gibali, A.; Reich, S.
2011
Fixed points of contractive functions. Zbl 0249.54026
Reich, Simeon
1972
Nonexpansive projections and resolvents of accretive operators in Banach spaces. Zbl 0383.47035
Bruck, Ronald E.; Reich, Simeon
1977
A weak convergence theorem for the alternating method with Bregman distances. Zbl 0943.47040
Reich, Simeon
1996
Some remarks concerning contraction mappings. Zbl 0211.26002
Reich, Simeon
1971
Nonexpansive iterations in hyperbolic spaces. Zbl 0728.47043
Reich, Simeon; Shafrir, Itai
1990
The split common null point problem. Zbl 1262.47073
Byrne, Charles; Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
Approximate selections, best approximations, fixed points, and invariant sets. Zbl 0375.47031
Reich, Simeon
1978
Asymptotic behavior of contractions in Banach spaces. Zbl 0275.47034
Reich, Simeon
1973
Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization. Zbl 0883.47063
Censor, Y.; Reich, S.
1996
Asymptotic behavior of relatively nonexpansive operators in Banach spaces. Zbl 1010.47032
Butnariu, D.; Reich, S.; Zaslavski, A. J.
2001
Proximinal retracts and best proximity pair theorems. Zbl 1054.47040
Kirk, W. A.; Reich, Simeon; Veeramani, P.
2003
Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space. Zbl 1232.58008
Censor, Yair; Gibali, Aviv; Reich, Simeon
2011
Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Zbl 1260.65056
Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
An iterative method for solving a class of nonlinear operator equations in Banach spaces. Zbl 0851.47043
Alber, Ya. I.; Reich, S.
1994
Projection and proximal point methods: Convergence results and counterexamples. Zbl 1059.47060
Bauschke, Heinz H.; Matoušková, Eva; Reich, Simeon
2004
Kannan’s fixed point theorem. Zbl 0219.54042
Reich, Simeon
1971
Weak convergence of orbits of nonlinear operators in reflexive Banach spaces. Zbl 1071.47052
Butnariu, Dan; Reich, Simeon; Zaslavski, Alexander J.
2003
A note on the multiple-set split convex feasibility problem in Hilbert space. Zbl 1171.90009
2007
Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Zbl 0849.47030
Bruck, Ronald; Kuczumow, Tadeusz; Reich, Simeon
1993
Some problems and results in fixed point theory. Zbl 0531.47048
Reich, Simeon
1983
Two strong convergence theorems for a proximal method in reflexive Banach spaces. Zbl 1200.47085
Reich, Simeon; Sabach, Shoham
2010
Fixed point theory in modular function spaces. Zbl 0714.47040
Khamsi, M. A.; Kozlowski, W. M.; Reich, S.
1990
Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces. Zbl 0427.47049
Nevanlinna, Olavi; Reich, Simeon
1979
On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces. Zbl 0396.47033
Baillon, J. B.; Bruck, R. E.; Reich, S.
1978
Product formulas, nonlinear semigroups, and accretive operators. Zbl 0437.47048
Reich, Simeon
1980
Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces. Zbl 1226.47089
Reich, Simeon; Sabach, Shoham
2010
Iterative methods for solving systems of variational inequalities in reflexive Banach spaces. Zbl 1250.47064
Kassay, Gábor; Reich, Simeon; Sabach, Shoham
2011
Nonlinear semigroups, fixed points, and geometry of domains in Banach spaces. Zbl 1089.46002
Reich, Simeon; Shoikhet, David
2005
An iterative procedure for constructing zeros of accretive sets in Banach spaces. Zbl 0375.47032
Reich, Simeon
1978
Extension problems for accretive sets in Banach spaces. Zbl 0378.47037
Reich, Simeon
1977
A strong convergence theorem for a proximal-type algorithm in reflexive Banach spaces. Zbl 1180.47046
Reich, Simeon; Sabach, Shoham
2009
Fixed points in locally convex spaces. Zbl 0216.17302
Reich, S.
1972
Some fixed point problems. Zbl 0329.47019
Reich, Simeon
1975
Three strong convergence theorems regarding iterative methods for solving equilibrium problems in reflexive Banach spaces. Zbl 1293.47065
Reich, Simeon; Sabach, Shoham
2012
Approximating fixed points of nonexpansive mappings. Zbl 0856.47032
Reich, Simeon
1994
Existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces. Zbl 1245.47015
Reich, Simeon; Sabach, Shoham
2011
Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Zbl 0977.34061
Aizicovici, Sergiu; McKibben, Mark; Reich, Simeon
2001
On the asymptotic behavior of nonlinear semigroups and the range of accretive operators. Zbl 0457.47053
Reich, Simeon
1981
On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces. Zbl 0431.47034
Baillon, J. B.; Bruck, R. E.; Reich, S.
1978
A limit theorem for projections. Zbl 0523.47040
Reich, Simeon
1983
Almost convergence and nonlinear ergodic theorems. Zbl 0404.47032
Reich, Simeon
1978
Weak convergence theorems for asymptotically nonexpansive mappings and semigroups. Zbl 0983.47040
Falset, Jesús García; Kaczor, Wiesława; Kuczumow, Tadeusz; Reich, Simeon
2001
Genericity in nonlinear analysis. Zbl 1296.47002
Reich, Simeon; Zaslavski, Alexander J.
2014
Common solutions to variational inequalities. Zbl 1296.47060
Censor, Yair; Gibali, Aviv; Reich, Simeon; Sabach, Shoham
2012
Fixed points of condensing functions. Zbl 0252.47062
Reich, Simeon
1973
Krasnoselski-Mann iterations in normed spaces. Zbl 0712.47050
Borwein, Jonathan; Reich, Simeon; Shafrir, Itai
1992
Well-posedness of fixed point problems. Zbl 1014.47033
Reich, Simeon; Zaslavski, Alexander J.
2001
Nonexpansive retracts in Banach spaces. Zbl 1125.46019
Kopecká, Eva; Reich, Simeon
2007
Nonlinear evolution equations and nonlinear ergodic theorems. Zbl 0359.34059
Reich, Simeon
1977
The asymptotic behavior of the composition of two resolvents. Zbl 1075.47033
Bauschke, Heinz H.; Combettes, Patrick L.; Reich, Simeon
2005
Block-iterative algorithms for solving convex feasibility problems in Hilbert and in Banach spaces. Zbl 1167.90010
2008
An incomplete Cauchy problem. Zbl 0599.34078
Poffald, Esteban I.; Reich, Simeon
1986
On fixed point theorems obtained from existence theorems for differential equations. Zbl 0328.47034
Reich, Simeon
1976
The asymptotic behavior of firmly nonexpansive mappings. Zbl 0649.47043
Reich, Simeon; Shafrir, Itai
1987
Iterative averaging of entropic projections for solving stochastic convex feasibility problems. Zbl 0880.90106
Butnariu, Dan; Censor, Yair; Reich, Simeon
1997
Complex dynamical systems and the geometry of domains in Banach spaces. Zbl 1060.37038
Elin, Mark; Reich, Simeon; Shoikhet, David
2004
Bregman strongly nonexpansive operators in reflexive Banach spaces. Zbl 1284.47033
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2013
Iterative methods for approximating fixed points of Bregman nonexpansive operators. Zbl 1266.26023
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2013
Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative. Zbl 1119.47050
Bartz, Sedi; Bauschke, Heinz H.; Borwein, Jonathan M.; Reich, Simeon; Wang, Xianfu
2007
An explicit construction of sunny nonexpansive retractions in Banach spaces. Zbl 1096.47055
2005
Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces. Zbl 1028.47049
Alber, Yakov; Reich, Simeon; Yao, Jen-Chih
2003
The fixed point property for non-expansive mappings. II. Zbl 0443.47057
Reich, Simeon
1980
Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces. Zbl 1116.47052
Butnariu, Dan; Reich, Simeon; Zaslavski, Alexander J.
2006
Outer approximation methods for solving variational inequalities in Hilbert space. Zbl 1367.58006
Gibali, Aviv; Reich, Simeon; Zalas, Rafał
2017
The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces. Zbl 1339.47074
Bačák, Miroslav; Reich, Simeon
2014
Generic existence and approximation of fixed points for nonexpansive set-valued maps. Zbl 1183.47055
de Blasi, Francesco S.; Myjak, Józef; Reich, Simeon; Zaslavski, Alexander J.
2009
Semigroups and generators on convex domains with the hyperbolic metric. Zbl 0905.47056
Reich, Simeon; Shoikhet, David
1997
Accretive operators, Banach limits, and dual ergodic theorems. Zbl 0492.47030
Bruck, Ronald E.; Reich, Simeon
1981
A projection method for solving nonlinear problems in reflexive Banach spaces. Zbl 1206.47043
Reich, Simeon; Sabach, Shoham
2011
Right Bregman nonexpansive operators in Banach spaces. Zbl 1408.47011
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2012
The fixed point property for non-expansive mappings. Zbl 0336.47033
Reich, Simeon
1976
A characterization of Bregman firmly nonexpansive operators using a new monotonicity concept. Zbl 1221.26019
Borwein, Jonathan M.; Reich, Simeon; Sabach, Shoham
2011
Weak convergence of infinite products of operators in Hadamard spaces. Zbl 1348.47064
Reich, Simeon; Salinas, Zuly
2016
Approximating zeros of accretive operators. Zbl 0294.47042
Reich, Simeon
1975
Integral solutions to a class of nonlocal evolution equations. Zbl 1217.34103
García-Falset, Jesùs; Reich, Simeon
2010
Generation theory for semigroups of holomorphic mappings in Banach spaces. Zbl 0945.46026
Reich, Simeon; Shoikhet, David
1996
Generic aspects of metric fixed point theory. Zbl 1016.54021
Reich, Simeon; Zaslavski, Alexander J.
2001
A note on a mean ergodic theorem for nonlinear semigroups. Zbl 0521.47034
Reich, Simeon
1983
A note on the von Neumann alternating projections algorithm. Zbl 1066.46019
Kopecká, Eva; Reich, Simeon
2004
Constructing zeros of accretive operators. II. Zbl 0424.47034
Reich, Simeon
1979
Constructive techniques for accretive and monotone operators. Zbl 0444.47042
Reich, Simeon
1979
The Hundal example revisited. Zbl 1065.47048
Matoušková, Eva; Reich, Simeon
2003
Averaged mappings in the Hilbert ball. Zbl 0588.47061
Reich, Simeon
1985
Parametric representations of semi-complete vector fields on the unit balls in $$\mathbb{C}^ n$$ and in Hilbert space. Zbl 1036.32017
Aharonov, Dov; Elin, Mark; Reich, Simeon; Shoikhet, David
1999
The range of sums of accretive and monotone operators. Zbl 0423.47022
Reich, Simeon
1979
Asymptotic behavior of semigroups on nonlinear contractions in Banach spaces. Zbl 0337.47027
Reich, Simeon
1976
Convergence of generic infinite products of nonexpansive and uniformly continuous operators. Zbl 0932.47043
Reich, Simeon; Zaslavski, Alexander J.
1999
On the asymptotic behavior of nonlinear semigroups and the range of accretive operators. II. Zbl 0493.47034
Reich, Simeon
1982
Linearization models for parabolic dynamical systems via Abel’s functional equation. Zbl 1238.30010
Elin, Mark; Khavinson, Dmitry; Reich, Simeon; Shoikhet, David
2010
Reflexivity and approximate fixed points. Zbl 1054.46013
Matoušková, Eva; Reich, Simeon
2003
Fixed point theorems for set-valued mappings. Zbl 0423.47027
Reich, Simeon
1979
Random products of contractions in Banach spaces. Zbl 0735.47001
Dye, J.; Khamsi, M. A.; Reich, S.
1991
Iterating holomorphic self-mappings of the Hilbert ball. Zbl 0543.47049
Goebel, Kazimierz; Reich, Simeon
1982
The alternating algorithm of von Neumann in the Hilbert ball. Zbl 0768.41032
Reich, Simeon
1993
Convergence of Krasnoselskii-Mann iterations of nonexpansive operators. Zbl 0977.47046
Reich, S.; Zaslavski, A. J.
2000
New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings. Zbl 1465.65054
Reich, Simeon; Thong, Duong Viet; Dong, Qiao-Li; Li, Xiao-Huan; Dung, Vu Tien
2021
Inertial projection-type methods for solving pseudomonotone variational inequality problems in Hilbert space. Zbl 07401543
Reich, Simeon; Thong, Duong Viet; Cholamjiak, Prasit; Long, Luong Van
2021
Projection algorithms for solving the split feasibility problem with multiple output sets. Zbl 07403124
Reich, Simeon; Tuyen, Truong Minh
2021
An optimization approach to solving the split feasibility problem in Hilbert spaces. Zbl 07340876
Reich, Simeon; Tuyen, Truong Minh; Ha, Mai Thi Ngoc
2021
Fixed points and convergence results for a class of contractive mappings. Zbl 07399391
Reich, Simeon; Zaslavski, Alexander J.
2021
Finitely convergent iterative methods with overrelaxations revisited. Zbl 07419638
Kolobov, Victor I.; Reich, Simeon; Zalas, Rafal
2021
A new algorithm for solving the split common null point problem in Hilbert spaces. Zbl 07160103
Reich, Simeon; Tuyen, Truong Minh
2020
Parallel iterative methods for solving the split common fixed point problem in Hilbert spaces. Zbl 1442.47064
Reich, Simeon; Truong Minh Tuyen; Nguyen Minh Trang
2020
Weak, strong and linear convergence of the CQ-method via the regularity of Landweber operators. Zbl 1435.47063
Cegielski, Andrzej; Reich, Simeon; Zalas, Rafał
2020
Iterative methods for solving the generalized split common null point problem in Hilbert spaces. Zbl 1445.47043
Reich, Simeon; Truong Minh Tuyen
2020
Two projection methods for solving the multiple-set split common null point problem in Hilbert spaces. Zbl 07249879
Reich, Simeon; Tuyen, Truong Minh
2020
The split feasibility problem with multiple output sets in Hilbert spaces. Zbl 1460.90201
Reich, Simeon; Truong, Minh Tuyen; Mai, Thi Ngoc Ha
2020
Two projection algorithms for solving the split common fixed point problem. Zbl 07220280
Reich, Simeon; Tuyen, Truong Minh
2020
Existence of diametrically complete sets with empty interior in reflexive and separable Banach spaces. Zbl 1450.46008
Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon; Walczyk, Mariola
2020
Parallel iterative methods for solving the generalized split common null point problem in Hilbert spaces. Zbl 07258362
Reich, Simeon; Tuyen, Truong Minh
2020
Inexact orbits of nonexpansive mappings with nonsummable errors. Zbl 07188959
Reich, Simeon; Zaslavski, Alexander J.
2020
Outer approximation methods for solving variational inequalities defined over the solution set of a split convex feasibility problem. Zbl 1446.47062
Cegielski, Andrzej; Gibali, Aviv; Reich, Simeon; Zalas, Rafał
2020
A fixed point result for mean nonexpansive mappings. Zbl 07249885
Reich, Simeon; Zaslavski, Alexander J.
2020
Descent methods with computational errors in Banach spaces. Zbl 1452.90319
Reich, Simeon; Zaslavski, Alexander J.
2020
Means and convergence of semigroup orbits. Zbl 07285141
Grzesik, Aleksandra; Kaczor, Wiesława; Kuczumow, Tadeusz; Reich, Simeon
2020
Re-examination of Bregman functions and new properties of their divergences. Zbl 1407.52008
Reem, Daniel; Reich, Simeon; De Pierro, Alvaro
2019
Numerical range of holomorphic mappings and applications. Zbl 1437.30001
Elin, Mark; Reich, Simeon; Shoikhet, David
2019
Convergence of iterates of nonexpansive mappings and orbits of nonexpansive semigroups. Zbl 07053114
Grzesik, Aleksandra; Kaczor, Wiesława; Kuczumow, Tadeusz; Reich, Simeon
2019
A telescopic Bregmanian proximal gradient method without the global Lipschitz continuity assumption. Zbl 1427.90222
Reem, Daniel; Reich, Simeon; De Pierro, Alvaro
2019
Asymptotic behavior of a dynamical system on a metric space. Zbl 1435.37028
Reich, Simeon; Zaslavski, Alexander J.
2019
The Bolzano-Poincaré-Miranda theorem in infinite-dimensional Banach spaces. Zbl 1476.47042
Ariza-Ruiz, David; Garcia-Falset, Jesús; Reich, Simeon
2019
Fixed points of Legendre-Fenchel type transforms. Zbl 07036242
Iusem, Alfredo N.; Reem, Daniel; Reich, Simeon
2019
Linear convergence rates for extrapolated fixed point algorithms. Zbl 07007071
Bargetz, Christian; Kolobov, Victor I.; Reich, Simeon; Zalas, Rafał
2019
Convergence properties of dynamic string-averaging projection methods in the presence of perturbations. Zbl 1459.47023
Bargetz, Christian; Reich, Simeon; Zalas, Rafał
2018
Regular sequences of quasi-nonexpansive operators and their applications. Zbl 1391.41006
Cegielski, Andrzej; Reich, Simeon; Zalas, Rafał
2018
Solutions to inexact resolvent inclusion problems with applications to nonlinear analysis and optimization. Zbl 1401.90233
Reem, Daniel; Reich, Simeon
2018
Generic well-posedness of fixed point problems. Zbl 1394.47059
Reich, Simeon; Zaslavski, Alexander J.
2018
Generic well-posedness of the fixed point problem for monotone nonexpansive mappings. Zbl 1416.47002
Reich, Simeon; Zaslavski, Alexander J.
2018
Fixed points of polarity type operators. Zbl 06925409
Reem, Daniel; Reich, Simeon
2018
Well-posedness of fixed point problems for monotone nonexpansive mappings. Zbl 07304688
Reich, Simeon; Zaslavski, Alexander J.
2018
Outer approximation methods for solving variational inequalities in Hilbert space. Zbl 1367.58006
Gibali, Aviv; Reich, Simeon; Zalas, Rafał
2017
Weak, strong, and linear convergence of a double-layer fixed point algorithm. Zbl 1369.47072
Kolobov, Victor I.; Reich, Simeon; Zalas, Rafał
2017
Monotone contractive mappings. Zbl 1437.54066
Reich, Simeon; Zaslavski, Alexander J.
2017
Porosity results for sets of strict contractions on geodesic metric spaces. Zbl 1474.54062
Bargetz, Christian; Dymond, Michael; Reich, Simeon
2017
The optimal error bound for the method of simultaneous projections. Zbl 1381.41013
Reich, Simeon; Zalas, Rafał
2017
Convergence to approximate solutions and perturbation resilience of iterative algorithms. Zbl 1456.47030
Reich, Simeon; Zaslavski, Alexander J.
2017
Ergodic properties of random infinite products of nonexpansive mappings. Zbl 1383.47008
Reich, Simeon; Zaslavski, Alexander J.
2017
Metric convergence of infinite products of operators in Hadamard spaces. Zbl 1470.41032
Reich, Simeon; Salinas, Zuly
2017
Weak convergence of infinite products of operators in Hadamard spaces. Zbl 1348.47064
Reich, Simeon; Salinas, Zuly
2016
A modular string averaging procedure for solving the common fixed point problem for quasi-nonexpansive mappings in Hilbert space. Zbl 1348.47065
Reich, Simeon; Zalas, Rafał
2016
Two porosity theorems for nonexpansive mappings in hyperbolic spaces. Zbl 1326.54048
Reich, Simeon; Zaslavski, Alexander J.
2016
Growth estimates for the numerical range of holomorphic mappings and applications. Zbl 1367.47066
Bracci, Filippo; Levenshtein, Marina; Reich, Simeon; Shoikhet, David
2016
Domains of accretive operators in Banach spaces. Zbl 1440.47042
Garcia-Falset, Jesús; Muñiz-Pérez, Omar; Reich, Simeon
2016
A weak ergodic theorem for infinite products of holomorphic mappings. Zbl 1370.37015
Reich, Simeon; Zaslavski, Alexander J.
2016
A convex analytic inequality revisited. Zbl 1366.46061
Reich, Simeon; Wang, Xianfu
2016
Contractive set-valued mappings. Zbl 1410.47020
Reich, Simeon; Zaslavski, Alexander J.
2016
Iterative methods for solving variational inequalities in Euclidean space. Zbl 1332.47044
Gibali, Aviv; Reich, Simeon; Zalas, Rafał
2015
A remark on weakly contractive mappings. Zbl 1315.54025
Aguirre Salazar, Lorena; Reich, Simeon
2015
Approximate fixed points of nonexpansive set-valued mappings in unbounded sets. Zbl 1329.47058
Reich, Simeon; Zaslavski, Alexander J.
2015
Infinite products of discontinuous operators in Banach and metric spaces. Zbl 1435.47061
Reich, Simeon; Salinas, Zuly
2015
Variants of Caristi’s fixed point theorem. Zbl 1325.54046
Reich, Simeon; Zaslavski, Alexander J.
2015
Contractivity and genericity results for a class of nonlinear mappings. Zbl 1335.47034
Reich, Simeon; Zaslavski, Alexander J.
2015
Genericity and porosity in fixed point theory: a survey of recent results. Zbl 1347.54002
Reich, Simeon; Zaslavski, Alexander J.
2015
Infinite products of discontinuous operators. Zbl 1353.47024
Pustylnik, Evgeniy; Reich, Simeon
2015
Contractivity, porosity and infinite products. Zbl 1325.47097
Reich, Simeon; Zaslavski, Alexander J.
2015
Invariant sets of nonexpansive mappings. Zbl 06651357
Reich, Simeon; Zaslavski, Alexander J.
2015
Generic contractivity of nonexpansive mappings with unbounded domains. Zbl 1442.54047
Reich, Simeon; Zaslavski, Alexander J.
2015
The Denjoy-Wolff iteration property in the Hilbert ball. Zbl 1314.32006
Budzyńska, Monika; Reich, Simeon
2015
The common fixed point set of commuting holomorphic mappings in Cartesian products of Banach spaces. Zbl 1318.32003
Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon
2015
Limiting behavior of the Kobayashi distance. Zbl 1357.32016
Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon
2015
Genericity in nonlinear analysis. Zbl 1296.47002
Reich, Simeon; Zaslavski, Alexander J.
2014
The asymptotic behavior of a class of nonlinear semigroups in Hadamard spaces. Zbl 1339.47074
Bačák, Miroslav; Reich, Simeon
2014
Approximating fixed points in the Hilbert ball. Zbl 1344.32003
Kopecká, Eva; Reich, Simeon
2014
Porosity and the bounded linear regularity property. Zbl 1310.46025
Reich, Simeon; Zaslavski, Alexander J.
2014
Optimal pricing for optimal transport. Zbl 1296.49030
Bartz, Sedi; Reich, Simeon
2014
An example concerning bounded linear regularity of subspaces in Hilbert space. Zbl 1295.46018
Reich, Simeon; Zaslavski, Alexander J.
2014
Asymptotic behavior of inexact infinite products of nonexpansive mappings in metric spaces. Zbl 1307.47060
Reich, Simeon; Zaslavski, Alexander J.
2014
A generic fixed point theorem. Zbl 1333.47043
Gabour, Manal; Reich, Simeon; Zaslavski, Alexander J.
2014
Three generic results in holomorphic fixed point theory. Zbl 1385.47023
Reich, Simeon; Zaslavski, Alexander J.
2014
Some inequalities for the horosphere function and hyperbolically nonexpansive mappings on the Hilbert ball. Zbl 1341.32014
Elin, M.; Levenshtein, M.; Reich, S.; Shoikhet, D.
2014
Farthest points and porosity. Zbl 1309.41018
Boulos, Wissam; Reich, Simeon
2014
Bregman strongly nonexpansive operators in reflexive Banach spaces. Zbl 1284.47033
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2013
Iterative methods for approximating fixed points of Bregman nonexpansive operators. Zbl 1266.26023
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2013
Inner inclination of subspaces and infinite products of orthogonal projections. Zbl 1276.41028
Pustylnik, Evgeniy; Reich, Simeon; Zaslavski, Alexander J.
2013
An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space. Zbl 1296.47069
Cegielski, Andrzej; Gibali, Aviv; Reich, Simeon; Zalas, Rafał
2013
A note on Halpern’s algorithm in the Hilbert ball. Zbl 1323.47077
Reich, Simeon; Shemen, Lital
2013
Approximate fixed points of nonexpansive mappings in unbounded sets. Zbl 1300.47068
Reich, Simeon; Zaslavski, Alexander J.
2013
Finite element approximations of a nonlinear diffusion model with memory. Zbl 1276.65094
2013
Theorems of Denjoy-Wolff type. Zbl 1273.32004
Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon
2013
A Denjoy-Wolf theorem for compact holomorphic mappings in complex Banach spaces. Zbl 1305.46065
Budzyńska, Monika; Kuczumow, Tadeusz; Reich, Simeon
2013
Existence and approximation of fixed points of right Bregman nonexpansive operators. Zbl 1294.47073
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2013
Ergodicity, numerical range, and fixed points of holomorphic mappings. Zbl 1279.46028
Reich, Simeon; Shoikhet, David; Zemánek, Jaroslav
2013
A fixed point theorem for contractive non-self mappings. Zbl 1320.54045
Reich, Simeon; Zaslavski, Alexander J.
2013
Generic contractivity for a class of nonlinear mappings. Zbl 1300.47062
Reich, Simeon; Zaslavski, Alexander J.
2013
Algorithms for the split variational inequality problem. Zbl 1239.65041
Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
The split common null point problem. Zbl 1262.47073
Byrne, Charles; Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Zbl 1260.65056
Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
Three strong convergence theorems regarding iterative methods for solving equilibrium problems in reflexive Banach spaces. Zbl 1293.47065
Reich, Simeon; Sabach, Shoham
2012
Common solutions to variational inequalities. Zbl 1296.47060
Censor, Yair; Gibali, Aviv; Reich, Simeon; Sabach, Shoham
2012
Right Bregman nonexpansive operators in Banach spaces. Zbl 1408.47011
Martín-Márquez, Victoria; Reich, Simeon; Sabach, Shoham
2012
A von Neumann alternating method for finding common solutions to variational inequalities. Zbl 1263.47077
Censor, Yair; Gibali, Aviv; Reich, Simeon
2012
A note on alternating projections in Hilbert space. Zbl 1264.41033
Kopecká, Eva; Reich, Simeon
2012
Abstract convex optimal antiderivatives. Zbl 1259.47064
Bartz, Sedi; Reich, Simeon
2012
Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space. Zbl 1248.47052
Pustylnik, Evgeniy; Reich, Simeon; Zaslavski, Alexander J.
2012
Zone diagrams in compact subsets of uniformly convex normed spaces. Zbl 1256.52003
Kopecká, Eva; Reem, Daniel; Reich, Simeon
2012
...and 315 more Documents
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### Cited by 2,885 Authors

 206 Reich, Simeon 140 Kumam, Poom 92 Cho, Yeol Je 88 Shehu, Yekini 88 Yao, Jen-Chih 82 Qin, Xiaolong 79 Shahzad, Naseer 76 Zegeye, Habtu 68 Zaslavski, Alexander Yakovlevich 66 Ceng, Lu-Chuan 65 Takahashi, Wataru 64 Chang, Shih-Sen 64 Mewomo, Oluwatosin Temitope 61 Chidume, Charles Ejike 59 Xu, Hong-Kun 57 Cholamjiak, Prasit 56 Suantai, Suthep 53 Kang, Shin Min 52 Su, Yongfu 48 Dang Van Hieu 47 Dương Việt Thông 45 Bauschke, Heinz H. 45 Khamsi, Mohamed Amine 43 Yao, Yonghong 40 Kim, Jong Kyu 38 Agarwal, Ravi P. 38 Dong, Qiaoli 37 Abbas, Mujahid 37 Gibali, Aviv 36 Zhou, Haiyun 34 Marino, Giuseppe 34 Shoikhet, David 33 Jolaoso, Lateef Olakunle 33 Song, Yisheng 33 Trương Minh Tuyên 32 Liou, Yeongcheng 32 Petruşel, Adrian 31 Izuchukwu, Chinedu 31 Karapınar, Erdal 30 He, Songnian 30 Hussain, Nawab 30 Iyiola, Olaniyi Samuel 30 O’Regan, Donal 30 Wang, Shawn Xianfu 29 de la Sen, Manuel 29 Sintunavarat, Wutiphol 29 Wangkeeree, Rabian 28 Hamada, Hidetaka 28 Wen, Chingfeng 27 Censor, Yair 27 Djafari Rouhani, Behzad 27 Khatibzadeh, Hadi 26 Kohr, Gabriela 26 Saejung, Satit 25 Cho, Sun Young 25 Jung, Jong Soo 25 Kohlenbach, Ulrich Wilhelm 24 Ansari, Qamrul Hasan 24 Samet, Bessem 22 Kuczumow, Tadeusz 22 Latif, Abdul 22 Naraghirad, Eskandar 22 Wang, Lin 21 Basha, S. Sadiq 21 Bracci, Filippo 21 Cai, Gang 21 Combettes, Patrick L. 21 Du, Wei-Shih 21 Elin, Mark 21 Kazmi, Kaleem Raza 21 Radenovic, Stojan 21 Saewan, Siwaporn 21 Sahu, Daya Ram 20 Sunthrayuth, Pongsakorn 20 Vetro, Calogero 19 Altun, Ishak 19 Aydi, Hassen Mohamed 19 Chen, Rudong 19 Kimura, Yasunori 19 Suzuki, Tomonari 19 Tan, Bing 18 Iiduka, Hideaki 17 Ali, Bashir 17 Khan, Abdul Rahim 17 Kirk, William Arthur 17 Kozłowski, Wojciech M. 17 López Acedo, Genaro 17 Nashine, Hemant Kumar 17 Ogbuisi, Ferdinard Udochukwu 16 Abdou, Afrah Ahmad Noan 16 Alakoya, Timilehin Opeyemi 16 Cholamjiak, Watcharaporn 16 Garcia-Falset, Jesús 16 Graham, Ian R. 16 Panyanak, Bancha 16 Rehman, Habib Ur 16 Ugwunnadi, Godwin Chidi 15 Díaz-Madrigal, Santiago 15 Jleli, Mohamed Boussairi 15 Kangtunyakarn, Atid ...and 2,785 more Authors
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### Cited in 370 Serials

 457 Fixed Point Theory and Applications 271 Journal of Fixed Point Theory and Applications 261 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 256 Journal of Mathematical Analysis and Applications 160 Journal of Inequalities and Applications 152 Abstract and Applied Analysis 122 Optimization 96 Numerical Functional Analysis and Optimization 86 Nonlinear Analysis. Theory, Methods & Applications 81 Journal of Optimization Theory and Applications 81 Numerical Algorithms 74 Proceedings of the American Mathematical Society 71 Applied Mathematics and Computation 55 Computers & Mathematics with Applications 55 Journal of Nonlinear Science and Applications 54 Journal of Function Spaces 51 Journal of Global Optimization 49 Journal of Applied Mathematics 49 Thai Journal of Mathematics 45 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 42 Optimization Letters 38 Journal of Approximation Theory 37 Computational and Applied Mathematics 36 Rendiconti del Circolo Matemàtico di Palermo. Serie II 35 Journal of Computational and Applied Mathematics 33 Applied Mathematics Letters 31 Israel Journal of Mathematics 29 Bulletin of the Australian Mathematical Society 27 International Journal of Mathematics and Mathematical Sciences 25 Mathematical and Computer Modelling 24 Journal of Applied Mathematics and Computing 23 Transactions of the American Mathematical Society 23 Afrika Matematika 22 Set-Valued and Variational Analysis 22 Journal of Mathematics 21 Filomat 21 Mediterranean Journal of Mathematics 19 Applicable Analysis 19 Mathematical Programming. Series A. Series B 19 SIAM Journal on Optimization 19 Computational Optimization and Applications 18 Vietnam Journal of Mathematics 18 Optimization Methods & Software 18 Journal of Nonlinear and Variational Analysis 17 Results in Mathematics 17 The Journal of Analysis 17 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 16 Demonstratio Mathematica 16 Acta Mathematica Sinica. English Series 15 Journal of Functional Analysis 15 Topology and its Applications 15 Applied Mathematics and Mechanics. (English Edition) 15 Arabian Journal of Mathematics 15 AIMS Mathematics 14 Journal of Convex Analysis 14 Analysis and Mathematical Physics 13 Annali di Matematica Pura ed Applicata. Serie Quarta 13 Nonlinear Functional Analysis and Applications 13 Asian-European Journal of Mathematics 12 Journal d’Analyse Mathématique 12 Complex Analysis and Operator Theory 11 Acta Applicandae Mathematicae 11 Nonlinear Analysis. Modelling and Control 11 Nonlinear Analysis. Hybrid Systems 11 Applied General Topology 10 Proceedings of the Japan Academy. Series A 10 Applied Numerical Mathematics 10 Journal of Scientific Computing 9 Acta Mathematica Vietnamica 9 Advances in Mathematics 9 Journal of Differential Equations 9 Journal of Applied Analysis 9 Discrete Dynamics in Nature and Society 9 Fixed Point Theory 9 Boundary Value Problems 9 Journal of Industrial and Management Optimization 9 ISRN Mathematical Analysis 9 Journal of Linear and Topological Algebra 8 Inverse Problems 8 Automatica 8 Mathematische Annalen 8 Linear Algebra and its Applications 8 Journal of Mathematical Sciences (New York) 8 Mathematical Problems in Engineering 8 Advances in Difference Equations 8 Journal of Nonlinear Analysis and Optimization: Theory & Applications 8 Mathematics 8 Korean Journal of Mathematics 7 Applied Mathematics and Optimization 7 Calcolo 7 Czechoslovak Mathematical Journal 7 Integral Equations and Operator Theory 7 Zeitschrift für Analysis und ihre Anwendungen 7 Journal of the Australian Mathematical Society 7 International Journal of Analysis 7 Sahand Communications in Mathematical Analysis 6 Rocky Mountain Journal of Mathematics 6 Archiv der Mathematik 6 Journal of Soviet Mathematics 6 Journal of the Nigerian Mathematical Society ...and 270 more Serials
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### Cited in 56 Fields

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text:
# $G$ modulo $N$ is a cyclic group when $G$ is cyclic

If G is a cyclic group and N is a subgroup of G, show that G/N (or GmodN) is a cyclic group.

What I have so far: Since N is a subgroup of the cyclic group G, G/N is a cyclic group.

I think I'm missing details. What suggestions do you have?

-

The exact statement goes for this as it did for your last post, you haven't actually stated why the result is true, you just said it (sorry if I sound harsh). Moreover, the same question I stated last time, applies here. More generally if $C$ is cyclic and $f:C\to H$ is a surjective homomorphism then $H$ is cyclic. Why does this help us? Why is it true?

-
Thank you for responding. I didn't state why the result is true, because I don't know why yet. I'm not sure why that helps us. –  Lily Nov 3 '11 at 19:07
Because whenever you have a quotient group $G/N$ you have the canonical projection $\pi:G\to G/N$ (i.e. the map $g\mapsto gN$). So, anything preserved under homomorphisms is preserved when going from $G$ to $G/N$. For example, back my actual comment, why if $C=\langle c\rangle$ why does $H=\langle f(c)\rangle$? –  Alex Youcis Nov 3 '11 at 19:09

Explicitly: $G$ is isomorphic to either $\mathbb{Z}$ or $\mathbb{Z}_n$ for some $n\in\mathbb{Z_{\geq 2}}$.

In the first case, any subgroup is of the form $m\mathbb{Z}$ for some $m\in\mathbb{Z_{\geq2}}$ and so the quotient group is then isomorphic to $\mathbb{Z_m}$, which is cyclic.

In the second case, any subgroup of $\mathbb{Z}_n$ is isomorphic to $\mathbb{Z}_k$ where $k|n$. The quotient group $\mathbb{Z}_n/\mathbb{Z}_k$ is isomorphic to $\mathbb{Z}_{\frac{n}{k}}$ which again is cyclic.

So basically: all subgroups of cyclic groups are cyclic, and a cyclic group quotiented by a cyclic subgroup is again cyclic.

-

Now $G = \langle g \rangle$ and $N \trianglelefteq G$ since $G$ is abelian. Since $N$ is normal in $G$, the quotient group $G/N$ exists and it makes sense to wonder if it is cyclic. Then you can show that $G/N = \langle gN \rangle$.

-


text:
# Bessel filter

In analog filter technology, there are several basic types that are characterized by certain transmission properties and are used accordingly. These include the Bessel filter, named after the German mathematician Friedrich Bessel (1784-1846), the Butterworth filter and the Chebyshev filter.

The Bessel filter is characterized by a constant group delay and a linear phase behavior in the passband( DB) of the filter.

Attenuation and phase response as well as the group delay of Bessel filters.

The linear phase response results in a constant time delay of all frequencies transmitted in the passband. This property is particularly interesting for distortion-free transmission of broadband signals such as step signals, square-wave signals or pulses transmitted without overshoot and ringing. However, the slope is flatter than the other two types of filters mentioned.

To achieve a high stopband attenuation, Bessel filters require a higher filter order than other filters.

Informations:
 Englisch: Bessel filter Updated at: 19.03.2019 #Words: 142 Links: indium (In), analog, filter, transmission, Butterworth filter Translations: DE Sharing:


text:
# Formulas You’ll Need for the Accuplacer Next Generation Advanced Algebra and Functions Test

The following chart will give you the basic formulas you’ll need to ace the Advanced Algebra and Functions section of the Accuplacer Next Generation Test. You probably won’t be able to use this chart during this test, but it is an awesome tool for you to have an overview of the wide range of topics covered in this section.

These are the very basic equations, so feel free to also check out our more complete study guides, and solve our sample problems to hone your skills at Union Test Prep!

### Linear Equations

Formula Symbols Comments
$A\cdot x + B\cdot y = C$ $A, B, C = \text{any real number}$
$y= \text{dependent variable}$
$x = \text{independent variable}$
Standard Form
$y=m \cdot x + b$ $y = \text{dependent variable}$
$m= \text{slope}$
$x = \text{independent variable}$
$b = y \text{-intercept}$
Slope-Intercept Form. Try to convert linear equations to this format.
$m = \dfrac{y_2 - y_1}{x_2 - x_1}$ $m = \text{slope}$
$y_n = \text{dependent variable (point n)}$
$x_n = \text{independent variable (point n)}$
This is a rearranged version of the point-slope form.
$y-y_1 = m(x-x_1)$ $y= \text{dependent variable}$
$x = \text{independent variable}$
$y_1 = y \text{ value of a point on the line}$
$x_1 = x \text{ value of a point on the line}$
$m = \text{slope}$
Point-Slope form
$x+a = b \Rightarrow x = b-a$
$x-a = b \Rightarrow x = b+a$
$x \cdot a = b \Rightarrow x = b \div a$
$x \div a = b \Rightarrow x = b \cdot a$
$x^a = b \Rightarrow x = \sqrt[a]{b}$
$\sqrt[a]{x} = b \Rightarrow x = b^a$
$a^x = b \Rightarrow x = \dfrac{\log b}{\log a}$
$a, b = \text{constants}$
$x = \text{variable}$

### Quadratic Equations

Formula Symbols Comments
$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ $a,b = \text{constants}$
$c = \text{constant (y-intercept)}$
$x = \text{variable}$
Quadratic Formula for equation in the form $ax^2+bx+c=0$
$(a \pm b)^2 = a^2 \pm 2ab + b^2$ $a,b = \text{constants or variables}$ Square of a sum or difference
$a^2-b^2 = (a+b)\cdot (a-b)$ $a,b = \text{constants or variables}$ Difference of squares

### Cubic Equations

Formula Symbols Comments
$a^3-b^3 = (a-b) \cdot (a^2+ab + b^2)$ $a,b = \text{constants or variables}$ Difference of cubes
$a^3+b^3 = (a+b) \cdot (a^2-ab + b^2)$ $a,b = \text{constants or variables}$ Sum of cubes

### Geometry Equations

Formula Symbols Comments
$A = s^2$ $A = \text{area of a square}$
$s = \text{side length}$

$A = l \cdot w$ $A = \text{area of a rectangle}$
$l = \text{length}$
$w = \text{width}$

$A = \dfrac{1}{2} b \cdot h$ $A = \text{area of a triangle}$
$b= \text{base}$
$h = \text{height}$

$A = \pi \cdot r^2$ $A = \text{area of a circle}$
$r = \text{radius}$

$A = h \cdot \dfrac{b_1+b_2}{2}$ $A = \text{area of a trapezoid}$
$b_n = \text{base }n$
$h = \text{height}$

$C= 2 \pi r = \pi d$ $C = \text{perimeter of a circle}$
$r = \text{radius}$
$d = \text{diameter}$

$V = s^3$ $V = \text{volume of a cube}$
$s = \text{side length}$

$V = l \cdot w \cdot h$ $V = \text{volume of a rectangular prism}$
$l = \text{length}$
$w = \text{width}$
$h = \text{height}$

$V = \dfrac{4}{3} \pi r^3$ $V = \text{volume of a sphere}$
$r = \text{radius}$

$V = \pi r^2 h$ $V = \text{volume of a cylinder}$
$r = \text{radius of base}$
$h = \text{height}$

$V = \dfrac{1}{3} \pi r^2 h$ $V = \text{volume of a cone}$
$r = \text{radius}$
$h = \text{height}$

$V = \dfrac{1}{3} l \cdot w \cdot h$ $V = \text{volume of a pyramid}$
$l = \text{length}$
$w = \text{width}$
$h = \text{height}$

$d= \sqrt{\mathstrut (y_2 - y_1)^2 + (x_2-x_1)^2}$ $d = \text{distance between two points}$
$y_n = y \text{ value at point n}$
$x_n = x \text{ value at point n}$

$a^2 + b^ 2 = c^ 2$ $a,b = \text{legs of a right triangle}$
$c = \text{hypotenuse of a right triangle}$
Pythagorean theorem
$(x-h)^2 + (y-k)^2 = r^2$ $(h,k) = \text{center of a circle}$
$r = \text{radius}$
Standard form of a circle
$x^2 + y^2 + Ax + By + C = 0$ $x, y = \text{variables}$
$A,B,C = \text{constants}$
General form of a circle

### Trigonometry Equations

Formula Symbols Comments
$\sin^2 \theta + \cos^2 \theta = 1$   Pythagorean Identity
$\sin 2\theta = 2 \sin \theta \cdot \cos \theta$
$\cos 2\theta = \cos^2 \theta - \sin^2 \theta = 2 \cos^2 \theta -1$
$\tan 2\theta = \frac{2 \tan \theta}{1-\tan^2 \theta}$
Double Angle formulas

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text:
# A characterization of Cauchy filters on countable metric spaces?

Given a filter $\mathcal F$ on a countable set $X$, consider the family $$\mathcal F^+:=\{A\subset X:\forall F\in\mathcal F\;(A\cap F\ne\emptyset)\}.$$

The following characterization is well-known.

Theorem S. A filter $\mathcal F$ on a countable set $X$ is not an ultrafilter if and only if the family $\mathcal F^+$ contains two disjoint sets.

A topological counterpart of this theorem is less known and holds for analytic filters. Let us recall that a filter $\mathcal F$ on a countable set $X$ is analytic if it is analytic (i.e., a continuous image of a Polish space) as a subspace of the power-set $\mathcal P(X)$ endowed with the natural compact metrizable topology.

Theorem T. An analytic filter $\mathcal F$ on a countable topological space $X$ is divergent if and only if the family $\mathcal F^+$ contains two disjoint closed subsets of $X$.

This theorem can be (more or less) easily proved using Talagrand's characterization of meager filters.

Now the question: Is the following metric counterpart of Theorems S and T true?

Conjecture M. An analytic filter $\mathcal F$ on a countable metric space $(X,d)$ is not Cauchy if and only if the family $\mathcal F^+$ contains two sets $A,B$ with positive distance, i.e., such that $d(A,B):=\inf\{d(a,b):a\in A,\;b\in B\}>0$.

Remark. Conjecture M is true for metric spaces which are uniformly homeomorphic to subspaces of $\mathbb R^\omega$ endowed with the natural uniformity. In particular, it is true for totally bounded metric spaces.

On the other hand, the unit ball of an infinite-dimensional Banach space is not uniformly homeomorphic to a subspace of $\mathbb R^\omega$.


text:
# Nonnegative signed total Roman domination in graphs

Document Type : Original paper

Authors

1 Sirjan University of Technology, Sirjan 78137, Iran

2 RWTH Aachen University

Abstract

Let $G$ be a finite and simple graph with vertex set $V(G)$. A nonnegative signed total Roman dominating function (NNSTRDF) on a graph $G$ is a function $f:V(G)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N(v)}f(x)\ge 0$ for each $v\in V(G)$, where $N(v)$ is the open neighborhood of $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has a neighbor $v$ for which $f(v)=2$. The weight of an NNSTRDF $f$ is $\omega(f)=\sum_{v\in V (G)}f(v)$. The nonnegative signed total Roman domination number $\gamma^{NN}_{stR}(G)$ of $G$ is the minimum weight of an NNSTRDF on $G$. In this paper we initiate the study of the nonnegative signed total Roman domination number of graphs, and we present different bounds on $\gamma^{NN}_{stR}(G)$. We determine the nonnegative signed total Roman domination number of some classes of graphs. If $n$ is the order and $m$ is the size of the graph $G$, then we show that $\gamma^{NN}_{stR}(G)\ge \frac{3}{4}(\sqrt{8n+1}+1)-n$ and $\gamma^{NN}_{stR}(G)\ge (10n-12m)/5$. In addition, if $G$ is a bipartite graph of order $n$, then we prove that $\gamma^{NN}_{stR}(G)\ge \frac{3}{2}\sqrt{4n+1}-1)-n$.

Keywords

#### References

[1] N. Dehgardi and L. Volkmann, Signed total Roman k-domination in directed graphs, Commun. Comb. Optim. 1 (2016), no. 2, 165–178.
[2] N. Dehgardi and L. Volkmann, Nonnegative signed edge domination in graphs, Kragujevac J. Math. 43 (2019), no. 1, 31–47.
[3] N. Dehgardi and L. Volkmann, Nonnegative signed Roman domination in graphs, J. Combin. Math. Combin. Comput. (to appear).
[4] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in Graphs, Advanced Topics, Marcel Dekker, Inc., New York, 1998.
[5] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York,
1998.
[6] L. Volkmann, Signed total Roman domination in graphs, J. Comb. Optim. 32 (2016), no. 3, 855–871.
[7] L. Volkmann, Signed total Roman domination in digraphs, Discuss. Math. Graph Theory 37 (2017), no. 1, 261–272.
[8] L. Volkmann, Signed total Roman k-domination in graphs, J. Combin. Math. Combin. Comput. 105 (2018), 105–116.


text:
# libgdx sprite placement

Im making a soccer game where you basically have to shoot the ball to the goal and the ball goes to where you touch the screen. Im having an issue with the ball though, when the ball spawns on the player it goes directly to the top left corner of the screen, without even touching the screen. This might be really easy but I cant seem to find the solution

Here's the code:

Ball class

public void shootToward(float targetX, float targetY) {

velocity.set(targetX - position.x, targetY - position.y);
}

public void update(float deltaTime) {

position.add(velocity.x * deltaTime, velocity.y * deltaTime);
velocity.scl(1 - (1f * deltaTime));
}

Game class

public void create () {

cam = new OrthographicCamera();
cam.setToOrtho(false, Gdx.graphics.getWidth(), Gdx.graphics.getHeight());
batch = new SpriteBatch();
batch.setProjectionMatrix(cam.combined);

player = new Sprite(player1);
player.setX(MathUtils.random(Gdx.graphics.getWidth()));
player.setY(MathUtils.random(Gdx.graphics.getHeight() / 2));

b.position.set(player.getX(), player.getY());

}

public void render () {
Gdx.gl.glClearColor(255, 255, 255, 1);
Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT);

b.update(Gdx.graphics.getDeltaTime());

batch.begin();
batch.draw(bg, 0, 0);
batch.draw(goal1, Gdx.graphics.getWidth()/4-20, Gdx.graphics.getHeight() - 180, 420, 130);
if (!Gdx.input.isTouched()) {
batch.draw(bs, b.position.x, b.position.y);
b.shootToward(Gdx.input.getX(), Gdx.graphics.getHeight() - Gdx.input.getY());
}
player.draw(batch);
batch.end();
}

My guess is that you have a stray ! in your code. Remove the ! in:
if (!Gdx.input.isTouched()) {

This is making it so shootToward() is being called when the player is not touching the screen.
• thanks it was actually pretty simple I ended up just doing this: if (!Gdx.input.isTouched()) { batch.draw(bs, b.position.x, b.position.y); }else if (Gdx.input.isTouched()) b.shootToward(Gdx.input.getX(), Gdx.graphics.getHeight() - Gdx.input.getY()); – gafflx May 4 '16 at 9:54


text:
# Carbon 11 radiolabeled inhaled Beta-2 agonist or corticosteroids, is it possible?

Background Positron emission tomography (PET) is a highly sensitive imaging modality that can provide in vivo quantitative information of biological processes at a biochemical level. PET relies upon the administration of a chemical probe, often called a radiopharmaceutical, that is labeled with a short-lived positron-emitting radionuclide, examples of which are $$\ce{^{11}C} \ (t_{1/2} = \pu{20.4 min})$$ and $$\ce{^{18}F} \ (t_{1/2} = \pu{109.7 min})$$. Carbon-11 is one of the most useful radionuclides for PET chemistry, since its introduction into a biologically active molecule has minimal effects on the (bio)chemical properties of the compound (Ref.: Dahl, et al., Clin. Transl. Imaging 2017, 5, 275–289)

Biologicals of interest Beta-2-Agonists are effective bronchodilators due primarily to their ability to relax airway smooth muscle (ASM). They exert their effects via their binding to the active site of b2-ARs, which are densely located on ASM. The presumed cellular mechanism of action involves the canonical signaling pathway via activation of Adenylyl cyclase (AC) and generation of intracellular cAMP, which in turn can activate the effector molecules cAMP-dependent protein kinase A (PKA) and Epac, a Rap1 guanine nucleotide exchange factor. However, there is still little known regarding these pathways in airway cells (Ref.: Am J Respir. Crit. Care Med. 2013, 187(7), 690–696).

Question Currently radiolabeled lung studies use labeled drugs that are produced for inhalation are "association” products, that is, the label is associated with the drug but not firmly bound to the drug. Without a firm bond between the active pharmaceutical ingredient (API) and the radiotracer, images must be acquired immediately post-inhalation before the dissociation of the label from the drug leads to a circulating level of absorbed radioactivity that could introduce an unacceptable error in the measurement of radioactivity in the lung. Carbon-11 radiolabeled ICS or Beta-2 agonists would enhance our understanding of the cellular mechanism of action. Anyone aware of work in this area?

References:

1. Kenneth Dahl, Christer Halldin, Magnus Schou, "New methodologies for the preparation of carbon-11 labeled radiopharmaceuticals," Clinical and Translational Imaging 2017, 5, 275–289 (DOI: https://doi.org/10.1007/s40336-017-0223-1).
2. Mario Cazzola, Clive P. Page, Paola Rogliani, M. Gabriella Matera, "$$\beta_2$$-Agonist Therapy in Lung Disease," Am. J. Respir. Crit. Care Med. 2013, 187(7), 690–696 (DOI: https://doi.org/10.1164/rccm.201209-1739PP).
• What does ICS stand for? Apr 27 at 11:13
• @orthocresol: ICS stands for " inhaled corticosteroid"! (from Ref.2 sighted) Apr 27 at 11:46
• It might be possible. But very hard as it would require a very rapid process (ie one taking significantly less time than the half life) to synthesise and isolate a complex molecule. That's not easy, even less so for steroids than beta-agonists. Apr 27 at 16:50

Positron emission tomography (PET) has been taken using $$\ce{^{11}C}$$- and $$\ce{^{18}F}$$-labelled reagents, although they are not $$\beta_2$$-agonists (Ref.1). The abstract states that:
It is clear that unto 2007, there are no evidence for the use of radiolabeled $$\beta_2$$-agonist or corticosteroids for PET in literature. However, there are other radiolabeled reagents have been use for the imaging. For instance, the mixed-venous content is obtained by imaging the right heart during the infusion, and the alveolar concentration is obtained by imaging the lung, after the blood volume is subtracted from the image using a separate $$\ce{^{11}C}$$-labeled carbon monoxide ($$\ce{^{11}CO}$$) inhalation.


text:
A puzzle with a story

Dick Karp needs no introduction. So I will give him none. Okay I will say that it has been an honor to know him for many years—we met right after I graduated from CMU, a pleasure to work with him on a few projects, and always fun to see.

Today I wish to talk about a recent dinner conversation I had with Dick and Noga Alon.

The dinner was the Simons advisory committee dinner this last Friday. At some point we were talking about stories of our kids. I was sitting between Dick and Noga. I had just talked about my daughter Jen, when Dick told a story about a phone call he once made to his son, years ago.

Dick was on a trip for business and called home to say hi to his son, Jeremy. His son asked, after some chit-chat:

Well Zack’s mom did.

Karp said that was it. Forget about the talk he had to give the next day, about other work, about research, he had to solve the puzzle. Note: I do not think it mattered that it was Zack’s Mom or Dad, just that it was solved by someone. As a father I can imagine, my reaction would have been the same. If Jen had said ${\dots}$

## The Puzzle

The problem is an innocent question about labeling a hexagon. The problem is to assign the integers ${1,2,\dots,12}$ to the twelve vertices and edges of the hexagon, so each number is used exactly once. So far pretty easy: there are six edges and six vertices so twelve numbers is just right. The catch—the reason it is a “puzzle”—is that the each edge must have the same “magic sum.” The magic sum is the sum of the numbers assigned to the edge plus the numbers assigned to its two endpoint vertices.

## Dick Solves The Problem

Dick said that he did find a solution that night. He told us that he first found an argument, which he could not recall, that the common value was ${19}$. He then used a kind of simulated annealing to find the solution. He put the twelve numbers down, then moved them to reduce the number of bad edges, ones with a sum different from ${19}$. He did this by hand, and was eventually able to solve the problem. He did not tell us whether he found the solution in seconds, minutes, or hours.

Noga started to sketch on a napkin a hexagon and we tried to figure out what the common number had to be. I gave a trivial lower bound, but we could not see why it had to be ${19}$. Noga had some idea that sounded likely to pin this down, yet we could not finish it. Noga also suggested that you could “write a program.” Indeed ${12!}$ is large, but not impossible for a laptop to handle. I thought that a search could be done more like

$\displaystyle \binom{12}{6} 6! 6!,$

which I believe is better. But Dick said that it could be done by hand. The dinner ended with me heading off to my hotel to get some rest. I do not know if Dick and Noga finished solving the problem once I left—I would not be surprised if they did.

## The Solution

When I started to write this piece I thought that I should first get a solution to the problem. I could have tried to do it by hand, or written a program as Noga suggested, but I used another method: Google search.

The problem sounded to me related to another notorious open problem called the graceful graph conjecture—more on that in a bit. I was wrong about that connection, they do not seem to be related in any obvious way. However, the hexagon problem has been studied since at least 1970. The general problem is: Given an undirected graph ${G=(V,E)}$, find a labeling of the edges and vertices with the numbers

$\displaystyle 1,2,\dots, |V|+|E|,$

so each number is used exactly once, and the edges have the same magic sum. Again the magic sum of an edge is the sum of the number assigned to the edge plus the values assigned to its endpoints. Such labeling are called edge-magic labelings.

See the paper by Andrew Baker and Joe Sawada for some nice results and further references. Or see the book Magic Graphs by Alison Marr and Walter Wallis.

Unlike the case of a magic square, the fact that vertex numbers are used a different number of times from edge numbers makes it possible to have solutions with different common magic-sum values.
Here is one solution; there are I believe at least three with different common sums. Click it to see the answer.

Note, the common value here is ${20}$, but there are solutions with common value ${19}$ also.

## Open Problems

I believe that finding the number of edge-magic labelings is open: both in the sense of a fast algorithm and in the sense of an analytic solution. Even an asymptotic bound seems hard.

If you like interesting labeling problems there is another innocent sounding problem: Does every tree have a graceful labeling? This problem is notorious, is open now for about sixty years, and is only known for special types of trees and small ones, trees with at most ${35}$ vertices. It is called the graceful graph conjecture—see here. And good luck.

[fixed typo]

January 25, 2014 10:38 pm

Each number on a vertex contributes to two of the sums; each number on an edge contributes to one of the sums. So, if you take two times the sum of the vertex numbers, and add the edge numbers, you will get 6 times the magic sum. This is the same thing as summing all twelve numbers (getting 78), and adding the sum of the vertex numbers; you must get 6 times the magic sum when you do that. Since 78 is a multiple of 6, the sum of the vertex numbers must be a multiple of 6.

The smallest multiple of 6 you can get by adding six of the numbers is 24: 1+2+3+5+6+7 is one way. If the vertex numbers sum to 24, then the magic sum will be (78+24)/6=17. The largest multiple of 6 you can get by adding six of the numbers is 54: 6+7+8+10+11+12 is one way. If the vertex numbers sum to 54, then the magic sum will be (78+54)/6=22. So, the magic sum must be something from 17 to 22.

I can confirm that all six totals are possible. But I won’t spoil any more. 🙂

• January 26, 2014 3:00 am

For any solution \$x_1, \ldots,x_12\$ with magic sum M, one can take the solution \$13-x_1,\ldots,13-x_12\$ which has magic sum 39-M. Since 39 is odd, this means that there cannot be only one possible magic sum.

2. January 26, 2014 12:25 am

I found one solution by trial-and-error. One idle observation is that the set of solutions over the field Z/13Z is permuted by simultaneously multiplying all the elements by the diagonal action of (Z/13Z)^*. There are “distinct” solutions (over Z) that are in the same orbit of this action (two of them below the fold), but for a “silly” reason. I wonder how many orbits there are of this action? What about if one also throws in the obvious dihedral group action?

(spoiler below)
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—————-

(spoiler: please feel free to delete)

Multiplication by 12 mod 13 (i.e. subtracting each number from 13) transforms solutions over Z to other solutions over Z. This is a bit silly. Are there other pairs of solutions over Z that differ by multiplication in a “nontrivial” way?

__5_2_12
_6______4
8________3
_10_____9
__1_11_7

__8_11_1
_7______9
5________10
_3______4
__12_2_6

January 27, 2014 10:04 am

Another solution for 20

Notation: (number(v1),number(e), number(v2))

(1,11,8),
(8,2,10),
(10,4,6),
(6,9,5),
(5,3,12),
(12,7,1)

4. January 27, 2014 4:51 pm

A toy/puzzle related to this is icosoku http://en.wikipedia.org/wiki/Icosoku and http://www.amazon.com/Recent-Toys-IC2869-IcoSoKu/dp/B003AIKTPU

5. January 29, 2014 4:58 am

After writing the six magic sum equations, it is easy to see that the sum of odd-numbered vertices is in [21,78]. This helps to show that the magic sum can range from 17 to 26. Even in an exhaustive search based program, these equations and the magic sum interval can then be used to prune the search space significantly.

My quick and dirty python script shows that there are 240 different solutions with magic sums ranging from 17 to 22. The number of solutions for each magic sum is as follows:
36 17
12 18
72 19
72 20
12 21
36 22

An example solution with the magic sum of 17 and its proof is:

sum: 17 vertices and edges in order a1-a12: 1 10 6 4 7 8 2 12 3 9 5 11

check 17 =a1+a2+a3=sum= 17
check 17 =a3+a4+a5=sum= 17
check 17 =a5+a6+a7=sum= 17
check 17 =a7+a8+a9=sum= 17
check 17 =a9+a10+a11=sum= 17
check 17 =a11+a12+a1=sum= 17

An example solution with the magic sum of 22 and its proof is:

sum: 22 vertices and edges in order a1-a12: 12 6 4 7 11 1 10 3 9 5 8 2

check 22 =a1+a2+a3=sum= 22
check 22 =a3+a4+a5=sum= 22
check 22 =a5+a6+a7=sum= 22
check 22 =a7+a8+a9=sum= 22
check 22 =a9+a10+a11=sum= 22
check 22 =a11+a12+a1=sum= 22

In the a1-a12 representation, the odd indexes are for the vertices and the even indexes are for the edges.

• January 31, 2014 3:00 am

BTW, I did not remove solutions that are probably shifted versions of each other (due to the hexagon being a loop). My script assumes the vertex a1 is fixed. I will probably find time later to change my script to count unique solutions.

• February 1, 2014 11:21 pm

It is also possible to generalize this problem to any n-gon for n greater than 2.

• February 2, 2014 4:15 am

It seems the sequence for the number of solutions for each n greater than 3 is recorded as A145692 or “Number of unique vertex-magic total labelings on cycle C_n” in Oct 16, 2008 in the The On-Line Encyclopedia of Integer Sequences.

6. January 31, 2014 2:57 am

And a practical application is?

January 31, 2014 12:07 pm

Qasim

One of refs claims network application for labels, but unclear to me

• January 31, 2014 12:21 pm

I do respect knowledge given in solving this puzzle a lot. As a teacher of algorithms, number theory as related to cryptology, information theory to CS undergraduates, it is a constant struggle to maintain their attention in class. Students have constant access to social networks through their laptops and notebooks. In such situations real practical applications help a lot. A perfect example is explanation of negative weights on edges given by Prof. Sedgwick in his algorithm analysis II course from coursera. He connects negative cycles to arbitrage of currencies beautifully.

I face a similar problem teaching chinese remainder theorem. It is fascinating to be able to count the size of your army within an integer multiple, but is not very attractive to a lot of students. I have searched google for practical uses of this theorem but have not had much luck. Any references will be much appreciated.


text:
# Mathematician:Paul Friedrich Wolfskehl

## Mathematician

German physician with an interest in mathematics.

He bequeathed $100\,000$ marks (equivalent to $£ 1\,000\,000$ pounds in $1997$ money) to the first person to prove Fermat's Last Theorem.

By the time the prize was finally awarded to Andrew John Wiles on $27$ June $1997$, the monetary value of the award had dwindled to $£30\,000$.

German

## History

• Born: 30 June 1856 in Darmstadt
• Died: 13 September 1906 in Darmstadt