Two different biological processes – one that creates new tumour cells and one that redistributes the cells that already exist – are wrapped up in the words “proliferation” and “diffusion”. Mathematically they are represented by two different terms of the reaction-diffusion equation that is often used to model solid‐tumour growth. Keeping the biology and the mathematics separate helps to see why they are not the same thing.

1. What is meant by “cell proliferation”?
   • Biology: Prolifer...

У «три запроса в секунду» заканчиваются все общие ограничения API.
Для методов, которые позволяют вытаскивать много персональных данных, ВК накладывает дополнительные, «плавающие» лимиты – users.search как раз из таких.

Что происходит

1. Если за короткое время (несколько-десятков секунд) сделать примерно 25-40 обращений к users.search с одного токена/IP, на этот токен/IP вешается короткий «бан поиска».
2. Пока бан действует, метод возвращает count : 0, items : [] на любой за...

Short version

• Since version 11.3 NDSolve\StateData[…]is no longer an ordinary expression but an opaque “handle” that just stores a pointer to an internal C-structure. • As soon as that pointer is duplicated, e.g. byLinkWrite/LinkRead, or the object is reconstructed with Hold[…] /. … // ReleaseHold, the link between the Mathematica level and the C-level data is broken. • Anything that afterwards tries to use the damaged object ( NDSolve`Iterate, NDSolve`ProcessSolutions`, …...

MS-Deploy is not ignoring your XPath – it is ignoring the whole parameter because of the characters that the parameter value contains. A value that is supplied inline in a .SetParameters.xml file is allowed to contain only ordinary text.
If the string contains one of the four characters shown below MS-Deploy drops the parameter silently and the default value that was baked into the package stays in the file:

@    <    >    &

(The rule is documented in “How to: Use Deployment Parame...

Yes – deciding whether a 0/1 matrix can be turned into a Hankel matrix by independently permuting its rows and its columns is an NP-complete problem (so, unless P = NP, no polynomial-time algorithm exists).

Why the problem is in NP
If two permutations σ (of the rows) and τ (of the columns) are given it takes Θ(n²) time to build the rearranged matrix σ M τ and to verify that every north-east / south-west (skew) diagonal is constant, so the problem is in NP.

From Hankel to Toeplitz and back
...

You’re looking for “Immersion” by Aliette de Bodard.

1. Publication data
   • First published in Clarkesworld Magazine #69, June 2012
   • Reprinted in several “Year’s Best” anthologies
   • Winner of the 2013 Nebula Award for Best Short Story, finalist for the Hugo and the Locus Awards

2. Why it matches the description

   • Social split: the story contrasts the “Galactics”, the interstellar élite who rely on extremely sophisticated wearable/implanted expert-systems called immersers,...

The phenomenon you hope for cannot occur:

If the product X × Y has the homotopy type of a finite-dimensional CW–complex, then each factor X and Y already has the homotopy type of a finite-dimensional CW–complex (in fact of dimension ≤ dim(X × Y)). Hence no counter–example exists.

1. From “finite dimensional product’’ to “finite dimensional domination’’

...

Windows Hello does not work the same way as BitLocker, where you can pick an “encryption type”.
With Hello you are not encrypting a file that you later decrypt; instead you are

1. Creating a public / private key pair that is bound to (and can only be used by) the device’s TPM, and
2. Unlocking the private key with a “gesture” (PIN, fingerprint, face, iris …).

The fingerprint is only the gesture that releases the private key inside the TPM; it is never the secret that is sent to a log-o...

Yes – the bi-interpretability works far below full PA, and it has in fact been written down. One convenient place to find it is in

Richard Kaye, “Models of Peano Arithmetic”, Oxford Logic Guides 15, Oxford Univ. Press, 1991.

Section 14 (“The field of fractions of a discretely ordered ring”) contains

• Lemma 14.4: for every discretely ordered ring (M\models Q) (i.e. Robinson arithmetic; this is strictly weaker than (I!\Delta _0), hence weaker than EFA) the usual quotient constructi...

No – at the moment not a single smooth, proper, geometrically connected curve of genus ≥ 2 over an algebraically closed field of characteristic p > 0 is known for which the whole étale fundamental group has been determined.

What is known.

1. Genus 0: π₁(ℙ¹)=1 (the only finite étale covers of ℙ¹ are the trivial ones by the Riemann–Hurwitz formula).

2. Genus 1: For any abelian variety A (in particular for an elliptic curve E) over an algebraically closed field one can classify the finite ...

Short answer. Nobody knows. Whether the set of all finite plane-graphs is well-quasi-ordered under the minor relation that has to respect the fixed embedding (usually called map–minors or embedded minors) is an open problem.

Explanation.

1. What is meant by “respecting the embedding”.
   • We work with plane ( = embedded planar) graphs.
   • A minor operation is allowed to
   – delete a vertex or an edge,
   – contract an edge,
   but the contraction has to be perform...

The story you are thinking of is

“Return Journey” by J. T. McIntosh
(first published in Galaxy Science Fiction, June 1957; re-printed many times since, e.g. in The Best from “Galaxy” Vol. III, The Road to Science-Fiction 3, Great Science-Fiction Stories, and other 1960--1980s anthologies).

Outline that matches your memories

1. All–male deep-space survey ship
   • The vessel and its charts were damaged while on an outward mission, so the surviving crew have only a rough idea of where the S...

Write the n-th (ordinary) harmonic number in lowest terms as

            Hₙ = 1 + ½ + ⅓ + … + 1/n = Aₙ / Bₙ ,      gcd(Aₙ , Bₙ)=1 .  

The integers Aₙ are collected in OEIS A002805 and are sometimes called the “harmonic numerators”.
So far the values of n for which Aₙ is a (decimal) prime have been computed far beyond 10 000; the list that you quote agrees with what is presently known.

What has been proved?

1. (Wolstenholme 1862)
   For every prime p ≥ 5 we have
   A_{p...

Short answer
At the moment you cannot run CoffeeScript source files directly with node --experimental-modules and have them behave as native ES modules. The CoffeeScript command-line tool works by installing a “require hook” that on-the-fly compiles the .coffee file and then lets Node execute the resulting JavaScript as a CommonJS module.
The ES-module loader that Node exposes under --experimental-modules:

1. ignores require hooks completely, and
2. decides whether the file *o...

What you’re seeing is not a problem with the way you create the nodes – it is a SceneKit / SpriteKit / Metal bug that appears as soon as an SKEffectNode finds itself inside an SKScene that SceneKit renders with Metal (which is the default in iOS 10).
The numbers in the assertion tell the story:

rect.x 0 + rect.width 1080  -> 1080   (SpriteKit asks Metal to draw 1080 px wide)
must be <= 240              ->  240   (the render target SceneKit has actually
                            ...

Let
G = ⟨g⟩ = { g⁰ , g¹ , … , g^{q-1} } ⊂ ℤ*ₚ , |G| = q

and let

I = { 1 , 2 , … , ⌊p/k⌋-1 } ⊂ ℤ*ₚ .

We are asked for an exponent

x ∈ {1,…,q-1} (1)

such that

g^x (mod p) ∈ I . (2)

Size of the solution set

|I| ≈ p/k, so the fraction of the residues in G that lie in I is

ρ = |G ∩ I| / |G| ≈ (p/k) / (p–1) ≈ 1/k. (3)

Hence there are about

q / k (4)

different exponents ...

Short answer
No. After the very first kilobytes the large, easy-to-see biases get smaller, but they never vanish, they are not monotonic, and nothing is known (and nothing seems likely) that would let you point to a single number N and say “from here on the bias is minimal”. “RC4-drop-N” therefore has no magic value of N that turns RC4 into an unbiased generator – it only trades big early weaknesses for smaller later ones.

Long answer

1. Why the early bytes are so bad
   • The Key‐Sc...

Short answer. No. Shrinking the time- or space-bound of the verifier to anything that is even mildly non-trivial (logarithmic space, NC circuits, etc.) does not decrease the power of the model: with these restricted verifiers you still obtain exactly the class NP. In other words

    NP = L-PCP(log n , 1) = NC¹-PCP(log n , 1) = …  

Consequently, to get a PCP characterisation of a class genuinely smaller than P one would have to restrict some other parameter (for example the amount of r...

Short answer
Nobody knows. The best lower bound we have for an (oblivious) comparator / sorting-network that outputs the median is Ω(n) comparisons, while the best upper bound that is known is still O(n log n). Whether the two bounds can be closed, i.e. whether Θ(n) comparators are sufficient, has been an open problem for more than thirty years.

Details

1. What ...

Yes – a local, deterministic “update rule’’ that is applied simultaneously to every tile of a Penrose tiling can simulate an arbitrary Turing machine. In other words there are Penrose-tiling cellular automata (PT-CA) that are universal in exactly the same sense as the usual, square–grid cellular automata such as Conway’s Life. Below is a sketch of a construction, an explanation of why the quasi-periodicity of the Penrose tiling does not cause any difficulty, and pointers to the literature wher...

Let M be a two–way probabilistic one–counter automaton (2P1CA) that works with bounded error, say it accepts every word w that is in the language with probability ≥ 2/3 and rejects every other word with probability ≥ 2/3.
Fix an input word w of length n.
During the run of M on w a configuration consists of

• the finite control state of M (|Q| possibilities)
• the current head position i (0 ≤ i ≤ n-1)
• the content of the counter c ∈ ℕ .

Thus a configuration can be written as (q,i,c). ...

Let

• H = Hét(–, ℚp) : Var/ℚp → Vecℚp
• HdR = Hdr(–/ℚp) : Var/ℚp → Vecℚp

be the two Weil co-homology theories on smooth projective ℚp–varieties that you fixed. Put

Perp := Isom⊗(H, HdR)

(the affine ℚp-scheme whose R-valued points are the tensor-compatible, graded, cup–product–, orientation– and cycle–class-preserving natural isomorphisms
H⊗ℚpR ≃ HdR⊗ℚpR).

1. What is already known?

a) Fontaine–Faltings (and, in the generality you want, Tsuji) give a canonical comp...

Let

S(a ,b ,c ) = a/(b+c) + b/(a+c) + c/(a+b)

and

C = { n ≥ 1 : ∃ a ,b ,c ≥ 1  S(a ,b ,c ) = n } .

1. The problem is equivalent to a single polynomial equation

   F(a ,b ,c ,n) = 0 ,

   where F is obtained by clearing the denominators:

   a(a+b)(a+c) + b(a+b)(b+c) + c(a+c)(b+c)
   

   – n (a+b)(a+c)(b+c) = 0 .

   Expanding, F is an integral polynomial of total degree 3 in the variables a ,b ,c (and of degree 1 in n, so of total degree 4 if n is counted as a variab...

Yes. Long before Aruḷnandi Śivācārya (13 th c.) wrote the passage you quote, Indian authors of many different schools already spoke of living creatures that suddenly “burst forth” from wood, earth or even solid stone. The two examples he gives—“worms in the heart of trees” and “toads in the heart of rocks” —were in fact stock illustrations that Indian philosophers, physicians and lexicographers had been using for at least fifteen hundred years.

1. The four ways of birth
   The oldest India...

The present state of knowledge is the following.

1. Nobody knows a single example of two non-isomorphic torsion–free abelian groups whose rational group–algebra fields of fractions are isomorphic.
2. No proof is known that this can never happen.

In other words, the question is open.

Below is a summary of what is known and of the main ideas that have been tried.

A. Easy cases in which the answer is known to be “no”.

A1. Finite rank, free groups.
If G ≅ ℤ^r and H ≅ ℤ^s ,...

Short answer
There is at present no part of the Langlands programme – nor any other long–standing problem that the community had previously regarded as disconnected from logic and topos theory – whose solution relies in an essential way on the “topos-theoretic bridges’’ developed by Olivia Caramello. L. Lafforgue’s sentence you quote is therefore best read as an expression of hope rather than as a reference to existing achievements.

Below is some more detailed information (with references) s...

The difficulty is caused entirely by the decision to use algebraic (K)-theory of finite–dimensional algebras.
If one replaces “algebraic” by “topological” and works with (real, (\Bbb Z/2)-graded) (\mathrm C^{*})-algebras the whole picture becomes canonical and all the problems disappear.

1. the (K)-theory of a point is the non-connective 8-periodic spectrum (KO);

2. Morita–invertibility in the graded world is the same as invertibility under the graded spatial tensor p...

Let

  √2 = 1 . d1 d2 d3 …     (di ∈ {0 , 1 , … , 9})

be the ordinary decimal expansion of √2 and, for an integer b ≥ 11, put

  θb := Σn≥1 di b-n. (1)

In words: we keep the same infinite string of decimal digits, but now regard it as the base-b fractional expansion of a new real number θb.
The question is whether one can prove, for some (or any) b ≥ 11, that θb is transcendental.

1. What can be proved easily
   • The digits of a rat...

Short answer
– Nothing “mysterious’’ happened. Stallings did in fact write a short manuscript entitled

    J. R. Stallings,  *On a theorem of Brown about the union of open
    cones*  (1961, 18 pp., mimeographed, Princeton University)  

 but he never submitted it to the *Annals* (or anywhere else).  
 A photocopy remains in Stallings’ papers (Bancroft Library, University
 of California at Berkeley, carton 4, folder 17) and a scan is now
 available from the...

Yes – if the players are allowed to mix with finitely additive probability measures ( “charges’’ on the power set of F₂ ) the game always has a saddle point, hence a Nash equilibrium, no matter what subset
W ⊂ F₂ is chosen. In particular the phenomenon has nothing to do with amenability; it holds for every group and for every infinite two–person zero–sum matrix game once finitely additive mixed strategies are admitted.

Why it is always solvable

1. Strategy spaces.
   Let M := ba₁(F₂) b...

At the moment nobody knows a proof (or a counter–example) of the statement

“For all sufficiently large n the sign character has strictly more
negative values than every other irreducible character of S n”.

What is known is the following.

1. Computations.
   • With GAP/MAGMA one can list every irreducible character of S n and count on how many conjugacy classes it is negative.
   The calculation has been carried out independently by several people up to n = 32 (≈ 4·1...

Yes – after one restricts the variation of the metric to a fixed Kähler class, the Laplacian on functions still has a simple spectrum for a “generic’’ metric. In other words

For every compact complex manifold (M , J) and every Kähler class [ω0], the set
G = { ϕ ∈ C∞(M)/ ℝ : ωϕ := ω0 + i∂∂̄ϕ is Kähler
and all non–zero eigenvalues of Δϕ are simple } is residual (a countable intersection of open dense sets) in the space of C∞ Kähler potent...

Short answer
Yes. Both questions have already been settled in the affirmative.
For an orientable Haken 3-manifold one can algorithmically produce a finite presentation of its mapping–class group, and from this decide

(a) whether the manifold possesses an orientation–reversing self-homeomorphism, and

(b) whether two given orientable Haken manifolds are homeomorphic by an orientation–preserving map.

Where to find it
The two standard places where the oriented problem is written out are

1...

No – the statement is already false in the smallest possible situation, namely for cyclic modules. A single counter-example is enough to show that the desired “algebraic saturation’’ property does not hold in general.

Notation. Throughout let 𝔬 be a DVR with maximal ideal 𝔭 and finite residue field 𝑘=𝔬/𝔭, and let the “type’’ of a finite 𝔬–module be the usual partition recording the exponents of its cyclic direct summands.

-----------------------------------------------------------------...

Yes – the factor that appears in the homogeneous direct integral L∞[0,1] ⊗̄ M completely determines the isomorphism class of the integral, no matter how big (or non–separable) the factors are. Hence, if

  L∞[0,1]  ⊗̄  M   ≅   L∞[0,1]  ⊗̄  N                                    (1)

then M ≅ N. A convenient way to see this is to use the standard central– (or direct–integral–) decomposition of a von Neumann algebra over its centre. Separability of the predual is not needed; what is used ...

Let k be a field of characteristic 0 and let

Stkᵑ(k) (n = 0,1,2,…,∞)

denote the category of n-Artin algebraic stacks of finite type over k whose diagonal is affine (0-stacks are varieties, 1-stacks are the usual Artin stacks, etc.).
For every n≥0 we put a “scissor’’–Grothendieck group on these stacks as follows (this is exactly the set-up used by B. Toën).

Definition. K₀(Stkᵑ) is the free abelian group generated by isomorphism classes [X] of n-stacks X∈Stkᵑ(k) subject to the three...

Let

 F(n) = the number of isomorphism classes of objects X of a finite–set structure F : C → FinSet with |F(X)| = n.

The question is whether we can get F(n) to be the (diagonal) Ackermann function
A(n,n), or at least some total computable function that grows faster than every primitive–recursive function.

1. A cheap way: “Yes”

For every total computable function g : ℕ→ℕ there is an entirely straightforward finite-set structure whose counting function is g. Fix such a g. Def...

Yes – the “effective” versions of the forcing notions that are used in recursion-/computability-theory can be described by exactly the same categorical recipe that one uses for ordinary set–theoretic forcing, the only difference being that one performs the construction

 “topos of sheaves on the forcing poset P”

not over the base topos Sets but over the effective topos Eff.
When the forcing site is interpreted internally to Eff the generic object that appears in the resulting sheaf topos ...

Let

P = {(x1 ,y1 ), … , (xn ,yn )}, n = m^2+1 , m ≥ 1
V = ( vαβ (j) ) ∈ ℝm^2×n , vαβ (j) = xjβ yjα , 0 ≤ α,β ≤ m−1.

(So the rows are all monomials yα xβ with α,β < m; there are m^2 rows.)

Goal
Describe Ker V and decide when it is one–dimensional.

1 Row rank and the geometric condition ——————————————————————————— Let

Πm = { bivariate polynomials p(x,y)=∑ α,β< m cαβ xβ yα } .

dim Πm = m^2 .
Writing the coefficients of p as the column vector cp = (c00 ,c01 ,…,cm−1,m−1...

Throughout let
 S­­₍F₎ = { x ∈ ℝ : 0 = a₁x^{e₁}+⋯+aₙx^{eₙ} for some n≥1 with pair-wise different exponents eᵢ∈F and non–zero coefficients aᵢ∈F }.
Put A₀ = ℚ and A_{n+1}=S(A_{n}).
The question is whether the inclusions A₀⊊A₁⊊A₂⊊… stay proper for every finite n, whether every A_{n} is a field, and whether numbers such as e ever lie in one of the A_{n}.

1. The first two steps
    A₁ is exactly the field of algebraic real numbers ℚ̄.

 Proof. If the exponents that occur are rational, wri...

Short answer
Yes, nothing contradictory is known to follow from the axiom

Stream_bisim A xs ys  ->  xs = ys

(or the analogous axiom for any other guarded co-inductive type).
In the usual set–theoretic model of Coq the axiom is actually true, so adding it to Coq can only be inconsistent if Coq itself already is.

Why the axiom is true in a classical model

1. How streams are interpreted.
   In the standard model (ZFC, sets in Set and propositions in Prop) the polymorphic str...

Write “Flex-term’’ for a (closed) expression that you can build out of

• the variable n, • decimal numerals 0,1,2,…, • the operations + , − , × , ÷ (ordinary rational division), • the unary symbol ⌊·⌋, and • the binary symbol ^ (exponentiation),

using the usual brackets to specify the order of evaluation.
The value of a Flex-term τ at n∈ℕ is the natural number that you obtain by carrying out the ordinary real‐number operations and taking the floor when a ⌊·⌋ occurs. The class 𝔽lex is t...

No – replacing the max–operator by a “draw-an-action-with-probability proportional to its current Q value’’ destroys the non-expansiveness that makes the usual Bellman optimality operator a γ–contraction.
The idea looks harmless – we only average the Q values instead of taking their maximum – but the weighting term itself depends on Q and can amplify differences between two Q–tables.

1. The operator that is obtained with Q–...

A straightforward way to obtain the value of

    1

I(m)= ───── ∬{-π}^{π} ∬{-π}^{π} 4π m cosx cosy – cosx – cosy ------------------------------------------------ dx dy (1) [ sin²x+sin²y+( m – cosx – cosy )² ]^{3/2}

is to look at it as an ordinary flux–integral and to keep track of the places where the denominator can vanish.
Everything can be done with nothing more than multivariable calculus, the divergence theorem and the elementary...

Let

  Φ(x)= 1/√(2π) ∫_{-∞}^{x} e^{-t²/2} dt (x∈ℝ)

denote the standard normal cumulative distribution function.
Put q₁∈ℚ*, q₂∈ℚ and assume

  Φ(q₁)=q₂. (1)

The question is whether (1) forces the “obvious’’ pair

  (q₁ , q₂)=(0 , 1/2).

Short answer. No proof of such a statement is known. In fact we do not even know how to prove that Φ(1), Φ(2) or Φ(1/10) is irrational. The only thing that is known unconditionally...

Let

    S(a , b)  :=  a^b + b^a          (  1 < a , b ∈ ℤ  ).

Trivially S(a , b) = S(b , a).
Your question is whether there are two different ordered pairs of integers

    (a , b) ≠ (m , n) ,     a , b , m , n  > 1 ,  a ≠ b , m ≠ n ,

such that (1)

    S(a , b) = S(m , n).

In other words, can the same integer be written as a^b + b^a in two essentially different ways?

1. A very easy family of “double” representations
   ...

Write

N = 4 ↑↑↑↑ 4

in ordinary arithmetic.
The first thing to notice is that every stage of the calculation keeps the base 4, so at the very end we again obtain a power of 4:

4 ↑↑ n = 4^(4 ↑↑ (n-1)) , therefore is a power of 4
4 ↑↑↑ n = 4 ↑↑ ( 4 ↑↑↑ (n-1) ) , hence a power of 4
…

Hence

N = 4 ↑↑↑↑ 4 = 4^K = (2^2)^K = 2^M (M = 2K).

Thus the problem is

“For the particular (enormous) exponent M, which decimal digit occurs
 most often in th...

The two passages you quoted correspond to two unrelated open questions that Federer left in his 1969 book. During the last fifty-odd years both questions have been examined in detail and their status is now well understood.

────────────────────────────────────────

1. §2.10.26 – The coarea–type inequality for a Lipschitz map
   ──────────────────────────────────────── Statement recalled from GMT (slightly simplified):

Let f : X → Y be a Lipschitz map between metric spaces,
A ⊂ X, 0 ≤ k, m ...

Short version
• With the iOS-7-and-earlier SDK there is no public (and therefore App-Store-legal) way to know when the hardware Ring/Silent switch is flipped or what position it is in.
• Every technique that really works relies on private frameworks or on polling side effects of those private frameworks; using any of them will get the application rejected.
• All you can (and should) do on iOS 7 is pick the proper audio-session category (Ambient / Solo-Ambient) so that your sound is automat...

No, nothing in the Intel/AMD instruction-set causes a loss of precision here.
What you have run into is a pure JIT-compiler error: when the JIT loads an ushort (or byte) value from a field and then has to widen it to 32 bits for a call to Vector128.Create, it sometimes uses a sign-extending conversion instead of the required zero-extending conversion. Consequently the value 0x8000 (32768u) is turned into 0xFFFF_8000 (-32768), and every calculation that depends on it becomes wrong...

Why the OS calls your view again after the app is already in the background

When the user presses the Home button iOS

1. sends your application the usual life-cycle messages
2. immediately takes an image of all the windows that are on-screen (this is the picture that is shown if the user re-enters the application without having killed it)
3. still while your process is alive, asks your view hierarchy to re-layout itself for every orientation / size class that might be neede...

Yes. Adding the usual axiom of (dependent) functional extensionality to Coq is believed to be sound whether Set is left predicative (the factory settings) or made impredicative with the flag -impredicative-set.

Why we are confident:

1. What the axiom says
   Functional extensionality is the sentence

   ∀ (A:Type) (B:A→Type) (f g : ∀x, B x),
        (∀x, f x = g x)  →  f = g .
   

(The usual non-dependent variant is the special case where B does no...

The statements you call A) and B) are unfortunately not true in general.
Below are two explicit counter-examples that violate them, followed by an explanation of why no “time–length versus profit” rule of the type you proposed can hold.

Notation that will be used:

Lk = log(xk) (the samples that are actually averaged)
Mk = (1/n) Σi=0…n-1 Lk-i (the n-point moving average of the logs)
t* = first instant that fulfils L t* ≤ M t* − d
t** = first instant after t* with ...

Short answer
No. In classical mechanics there is no extra “collision-term’’ that must be added to the action of a gas.
If the molecules interact through a pair potential

  V(r) = 0   for r > 2R
  V(r) = ∞  for r ≤ 2R (hard spheres)

then along every admissible trajectory one always has r>2R, so V≡0 and the action of N particles is simply

  S[ri(t)] = ∫dt ∑i ½ mi |v i|² . (1)

Impulsive chang...

Short answer
• Inside an ordinary λ-term that is represented as a tree you cannot have all three of

1. textual (tree-shaped) scopes,
2. the guarantee that each variable occurs only once, and
3. an operator that produces two independent copies of a term by doing only O (1) local work per reduction step.
   As soon as you start to “pull a λ out of the body’’ the occurrences of the variables it binds inevitably appear outside that λ, so the usual scope condition (every o...

The story you are looking for is
“The Pusher” by John Varley.

Why it matches your recollection

1. Released convict hired to assassinate a politician
   • The viewpoint character is an ex-con serving time on the remote penal colony at Charon.
   • Two well-connected “fixers” spring him from prison and give him a new identity on the sole condition that he kill a charismatic candidate who is about to become President of the Solar Confederation.

2. The hit takes place on a space stati...

The story you’re remembering is Wilson Tucker’s short novel / long novella
“The Year of the Quiet Sun” (first published in 1970; Hugo- and Nebula-award nominee).

How it matches the details you gave

1. How the protagonist gets into the future
   • Instead of cryogenic sleep, Army Captain Addison “Add” Douglass (an African-American Vietnam-era soldier) is one of a small U.S. government team that tests a brand-new time machine in 1978.
   • After a couple of short proving jumps he is sent a...

No trace of that passage can be found in any published science–fiction, fantasy, poetry or non-fiction source that predates December 1987.

What was checked

1. Full-text search engines (Google, Google Books, HathiTrust, Internet Archive, Project Gutenberg, SF-gateway, OpenLibrary) for individual expressions and for strings of three to seven consecutive words taken from every sentence (e.g.
   • “Forty thousand legions walked”
   • “desert of the moon in search of the land of Narda”
   •...

It sounds like your mother is remembering Arthur C. Clarke’s novelette “The Road to the Sea”.

What matches

1. A great green-glass highway
   • In Clarke’s story the “Road” is a broad strip of pale-green, glass-smooth, almost indestructible material that gleams like bottle-glass in the sun.
   • It was made with techniques long since lost; people can resurface or patch it, but no one can manufacture new sections of it.

2. Magnetic / very-high-speed transport
   • Traffic moves in gyro-ca...

It’s The Cloud Chamber by Howard L. Myers (Ballantine/Del Rey, 1977 — expanded from a shorter version that appeared in Analog in 1969).

Why it matches your memories

1. Earth has become a lifetime penal colony.
   • After the old Terran Empire lost a war with the “League,” the victors quarantined Earth behind an impenetrable energy screen and use it only as a dumping ground for convicts.
   • A single space-field in the foothills of the Rockies is the one legal landing place; freighters ...

Short answer
The current in–kernel hibernation code (swsusp / suspend-to-disk) does not contain, and has never contained, a facility that “remembers which pages were in RAM and puts them back there before userspace is thawed”. If a page had been pushed out to swap before you hibernate, it will still be in swap after you resume and it will be faulted back on demand, one page-fault at a time. There is no kernel configuration switch, boot parameter or run-time knob that changes this behavio...

The machine Ted Hoff was talking about was a Plessey System 250 (often written simply “P250” or “Plessey 250”).
A single–cabinet System 250 was delivered to Stanford University’s Digital Systems Laboratory in 1967 as a gift from Plessey and was still there when Hoff was doing graduate-student and post-doctoral work. In the oral-history interview he recorded for the Computer History Museum (CHM catalog number X5865.2010) he explains that

• the machine had “a couple of dozen fast registers tha...

The story you remember is “Pastmaster”, a Jeff Hawke adventure that ran as a daily newspaper strip in the British Daily Express from November 1967 to April 1968.

1. Series
   • “Jeff Hawke” – a long-running British SF strip written (for most of its classic period) by Willie Patterson and drawn by Sydney (Sid) Jordan.
2. Story title and publication dates
   • “Pastmaster” (sometimes written “Past-Master” in reprint lists)
   • Daily Express strip numbers 4911-5083, 15 Nov 1967 – 26 Feb...

As far as we know to-day the question is still open.
No one has yet produced a finite p-group which can be proved not to occur as the group of Fp–rational points of a connected unipotent algebraic Fp–group, but neither has anybody shown that every p-group does occur. What is known can be summarised as follows.

1. All abelian p-groups occur.
   Choose, for every non–negative integer m, the truncated Witt–vector group Wm. It is a connected unipotent algebraic group over Fp of dime...

Short version
In the 1940-60s a handful of university and Veterans / military hospitals in the United States (Mayo, Cleveland Clinic, Walter-Reed, Brooke Army, Fitzsimons, Philadelphia Naval, several VA hospitals, etc.) set up what the authors of the day called “hiatus-hernia clinics” or “hiatus-hernia centers”.
They were not free-standing institutions – they were simply special outpatient sessions inside an existing hospital in which every patient who had a radiographic diagnosis of a hiatu...

Short answer

At the moment the public version of Privateer’s Crow’s Nest does ​not​ give an engineer, flight-dynamics team or space-insurance underwriter anything they could not already buy from the established commercial SSA* suppliers or obtain (for free) from Space-Track / CelesTrak and the numerous visualisation sites that use those data. What it does offer is:

• a very slick, browser-based 3-D display that is free and needs no log-in, and
• the promise that “in a later release” more ...

The name is genuine, but it does not belong to the very early Iranian material that was crystallised by Ferdowsī in the Šāh-nāmeh.
Shād-u-kām / Shādkam / Shādkamān (شاد و کام ، شادکام ، شادکمان ; literally ‘Joy-and-Fulfilment’) is a place that occurs in the later “romance” or dāstān tradition – stories that were composed in Persian and, still more frequently, in Ottoman Turkish and Indo-Persian/Urdu between the 14th and the 19th centuries.
In those romances it is usually described as one of ...

Short answer
Yes – hydrophobic carbon powders (graphite, carbon black, graphene platelets, soot, etc.) can be used instead of hydrophobic silica to surround and isolate tiny droplets of water. The objects you obtain are, however, better described as “liquid marbles” than as the commercial product called “dry-water”, and several of their properties differ from the silica material.

1. How the material is formed
   • ...

1. The sequence definition of a polynomial appears for the first time at the very beginning of

Ernst Steinitz, «Algebraische Theorie der Körper»,
Journal für die reine und angewandte Mathematik 137 (1910), 167 – 309.

On p. 169 Steinitz writes (italics in the original)

»Wir verstehen unter einer formalen Reihe
a₀ + a₁x + a₂x² + … (aν ϵ K)
eine Folge (a₀ , a₁ , a₂ , …) von Elementen des Körpers K.
Die Reihe heißt Polynom, wenn nur endlich viele aν von Nul...

Short answer
No. Esters of trifluoroacetic acid are not nanomolar or femtomolar inhibitors of acetylcholinesterase (AChE); they are simply (and usually very good) substrates. They are turned over in the normal two-step acyl-enzyme mechanism, the acyl-enzyme lifetime is in the µs–ms range, and they leave the active site after one catalytic cycle. Kinetic constants that have been measured for 2,2,2-trifluoroacetylcholine (TF-ACh) or for aryl-trifluoroacetates are close to, or a little higher ...

The book you are trying to remember is “Beyond the Silver Sky” (original magazine title “Thunder Over Starhaven”) by the British pulp-SF writer Kenneth Bulmer.

Why it matches the details you list

1. Protagonist
   • Vic (sometimes “Vik”) Morgan is a Royal Air-Force fighter pilot who is shot down during the closing months of the Second World War and is entombed in an Alpine glacier.
   • In the late 21st century he is discovered, thawed out and revived.

2. “Up-grading” after revi...

Short answer
• D-Wave does not publish a per-qubit “fidelity” in the sense used for gate-based processors, because quantum annealers do not execute a sequence of unitary gates whose average error can be characterised with protocols such as randomized benchmarking.
• All qubits and couplers are factory- and field-calibrated automatically before the system is made available to users. The outcome of that calibration – a table that maps the user-programmed dimensionless numbers hᵢ , Jᵢⱼ to th...

Short answer
Nobody knows. The question whether every number field can be imbedded in a finite monogenic number field – i.e. whether for every number field K there exists a finite extension L/K whose ring of integers is of the form

  𝒪_L = ℤ[α] (a “power-integral basis”)

is at present an open problem.

A few facts that are known

1. Degrees 1, 2, 3.
   Every quadratic or cubic field is itself monogenic, so nothing new is needed in these degrees.

2. First coun...

For dimension 4 the question has not been settled – no‐one presently knows a necessary and sufficient condition that tells exactly when a compact topological 4–manifold is (homeomorphic to) a CW–complex. What is known can be summarized as follows.

1. The “easy” direction (already mentioned in the question).
   • If a 4–manifold is smoothable, Kirby showed that it possesses a finite handle decomposition.
   • A finite handle decomposition is, after forgetting the thickening of the handle...

It turned out not to be an academic “journal” article at all but rather a feature in the US news-stand magazine Science Fiction Age:

Jeffrey Henning
“Alien Tongues”
Science Fiction Age, Vol. 3 No. 4 (July 1995), pp. 60-67.

What it is
• Eight-page, photograph-illustrated survey of invented languages that turn up in written SF (and a few in film and television).
• The piece opens with Kilgore Trout/Philip José Farmer’s Venus on the Half-Shell, goes on to Carl Sagan’s Contact, then ranges...