## P=NP when number of input that gives 1 is bounded by polynomial

Suppose there exists some NP-complete problem such that the number of inputs that gives 1 as an output is bounded by a polynomial; that is, if the problem is $$f : \{0, 1 \}^* \to \{0, 1\}$$, then, for every $$n$$, $$|\{ x \in \{0, 1 \}^n : f(x) = 1\}| \leq p(n)$$ for some polynomial $$p$$. Then, I want to show that the existence of this problem implies $$P = NP$$. Is it somehow related to LEXSAT?

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## Using ScalingFunctions to ListPlot data in specific range and also to print FrameTicks with appropriate precision, gives strange fluctuations

Through the following code, we generate Tp1:

In:= tempPV = (   3 \[Pi]^(2/3) + 6 6^(2/3) P \[Pi] V^(2/3) -     6^(2/3) V^(     2/3) (-3 + Sqrt[       9 + (4 6^(2/3) \[Pi]^(4/3) q^2)/(        V^(4/3) \[Beta]^2)]) \[Beta]^2 +     3 6^(2/3) V^(     2/3) \[Beta]^2 Log[      1/6 (3 + Sqrt[         9 + (4 6^(2/3) \[Pi]^(4/3) q^2)/(V^(4/3) \[Beta]^2)])])/(   6 6^(1/3) \[Pi]^(4/3) V^(1/3));  In:= \[Beta]in = 0.01; \[Beta]fi = 100; \[Beta]st = 0.005; Table[   xlog[\[Beta]] = Log[10, \[Beta]]   , {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}];  In:= parap1 = {q -> 0.1, V4 -> 5000}; parap2 = {T2 -> 15, q -> 0.1, V2 -> 10000}; parap4 = {T4 -> 5, q -> 0.1, V4 -> 5000};  In:= Table[    pressp2[\[Beta]] =     P /. Solve[(tempPV - T2 == 0) /. V -> V2 /. parap2, P][];(*p1=   p2*)   pressp4[\[Beta]] =     P /. Solve[(tempPV - T4 == 0) /. V -> V4 /. parap4, P][];(*p3=   p4*)   Tp1[\[Beta]] =     T1 /. Solve[(tempPV - T1 == 0) /. V -> V4 /. parap1 /.         P -> pressp2[\[Beta]], T1][];   , {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}];  In:= mi =   Min[Table[Tp1[\[Beta]], {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]] ma = Max[Table[    Tp1[\[Beta]], {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}]]  Out= 11.9083  Out= 11.9083  In:= ListPlot[  Table[{xlog[\[Beta]],     Tp1[\[Beta]]}, {\[Beta], \[Beta]in, \[Beta]fi, \[Beta]st}],   ScalingFunctions -> {Rescale[#, {mi, ma}, {0., 1.}] &,     Rescale[#, {0., 1.}, {mi, ma}] &}, Joined -> True, Frame -> True,   FrameStyle -> Black,   BaseStyle -> {FontSize -> 14, PrintPrecision -> 11},   FrameLabel -> {"\!$$\*SubscriptBox[\(log$$, $$10$$]\) (\[Beta])",     "\!$$\*SubscriptBox[\(T$$, $$1$$]\)"}, RotateLabel -> False,   PlotStyle -> {Blue, Thickness[0.006]},   PlotRange -> {{-2, 2}, {mi, ma}}, Axes -> None, AspectRatio -> 0.8,   ImageSize -> 400, FrameTicks -> {{ticks, None}, {Automatic, None}}]  

The result is the following plot: As it is clear there is a strange fluctuation for $$log_{10}^{\beta}=1-2$$. As it should be a smooth decreasing plot, what is the origin of these fluctuations? How to fix this possibly numerical error?

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## Wolfram code gives protected error

So I’m making a sort of graph with 2 main points and I’ve inspired myself on the internet and this is the final piece of code. Unfortunately it gives me a “Protected” error on multiple occasions. How do I solve this?

In:= (*Ecuațiile,ecuațiile inițiale,conectorii și parametrii modelului.*) noOfAnimals = "aniFlow.noOfAnimals"; rate = "aniFlow.rate"; equation = {populationSize'[t] == rate[t],  populationSize[t] == noOfAnimals[t]}; initialEquation = {If[steadyState, populationSize' == 0,  populationSize == initialPopulationSize]}; connectors = {aniFlow \[Element] "PredatorPrey.Components.AnimalConnector",  steadyState \[Element] Booleans}; parameters = {"initialPopulationSize" -> 10, "steadyState" -> False}; mmodel = CreateSystemModel["Hare", Join[equations, initialEquations], t,  connectors, <|"ParameterValues" -> parameters|>] SystemModel[mmodel, "ModelicaDisplay"]   Out= CreateSystemModel["Hare",  Join[equations,  initialEquations], t, {aniFlow \[Element]  "PredatorPrey.Components.AnimalConnector",  steadyState \[Element]  Booleans}, <|"ParameterValues" -> {"initialPopulationSize" -> 10,  "steadyState" -> False}|>]  Out= SystemModel[ CreateSystemModel["Hare", Join[equations, initialEquations],  t, {aniFlow \[Element] "PredatorPrey.Components.AnimalConnector",  steadyState \[Element]  Booleans}, <|"ParameterValues" -> {"initialPopulationSize" -> 10,  "steadyState" -> False}|>], "ModelicaDisplay"]    (*Ieșirea  reprezintă versiunea de vizualizare text Modelica a modelului \ creat*)  In:= model Hare parameter Real initialPopulationSize = 10; parameter Boolean steadyState = false; Real populationSize; PredatorPrey.Components.AnimalConnector aniFlow; initial equation if steadyState then der (populationSize) = 0; else  populationSize = initialPopulationSize; end if; equation der (populationSize) = anyFlow.rate; populationSize = aniFlow.noOfAnimals; end Hare;  Out= Hare CreateSystemModel["Hare", Join[equations, initialEquations],  t, {aniFlow \[Element] "PredatorPrey.Components.AnimalConnector",  SteadyState \[Element]  Booleans}, <|"ParameterValues" -> {"initialPopulationSize" -> 10,  "steadyState" -> False}|>]  During evaluation of In:= Set::write: Tag Times in initialPopulationSize parameter Real is  Protected.  During evaluation of In:= Set::write: Tag Times in Boolean parameter steadyState is Protected.  Out= {initial (Derivative[(aniFlow."aniFlow.noOfAnimals")][t] ==  "aniFlow.rate"[t]),  initial ((aniFlow."aniFlow.noOfAnimals")[t] == "aniFlow.noOfAnimals"[t])}  Out= if steadyState then  During evaluation of In:= Set::write: Tag Times in der aniFlow.aniFlow.noOfAnimals is Protected.  Out= else  Out= {Derivative[(aniFlow."aniFlow.noOfAnimals")][t] ==  "aniFlow.rate"[t], (aniFlow."aniFlow.noOfAnimals")[t] ==  "aniFlow.noOfAnimals"[t]}  During evaluation of In:= Set::write: Tag Times in der initialPopulationSize is Protected. 

This code insert includes the errors as well.

PS: Please fix the code insert as it is garbage at the moment.

## What do you do when avoiding railroading just gives you stuck players?

I’m seeking some newbie GM advice. I’m an experienced rpg player, but am much less experienced as a GM

I was recently running an D&D 5e adventure, where the players would be investigating in a town that had some problems with trade caravans being attacked. They started at the local Sheriffs office who tipped them that a local relatively new thieving guild was active in the area. The thieving guild wasn’t raiding the caravans, but I thought it might add a little plot twist to get the guild involved. My thought was to have the PCs eventually figure out that the guild wasn’t behind the problem and would need to investigate the local country-side to discover the problem. I had a few encounters written out, but I wasn’t fully sure how the PCs would reach their end goal of figuring out the source of the problem. I guess I thought that over-planning would be railroading and I wanted to give the players some freedom.

The players were often confused and unsure what to do. There wasn’t quite the excitement I was hoping for. They were eventually invited to a parley with the thieves guild but were not sure what to do with the thieves, so eventually just attacked them. It was ok, but not spectacular.

What do you do when your players seem stuck?

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## MLS API (Extenal API) images directly display on website, it gives error of 403 forbidden

Images work well before few days but now it’s getting an error of 403 forbidden. How to solve this issue, make sure it’s external images path

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## DEigensystem gives x-dependent eigenvalues

I am considering the eigenvalue problem associated with the double-well harmonic oscillator. Using the DEigensystem

DEigensystem[-1/2 y''[x] + (-x^2/2 + x^4/4) y[x], y[x], {x, -\[Infinity], \[Infinity]}, 2] 

gives eigenvalues that depend on $$x$$

{Sqrt[-2 + x^2]/(2*Sqrt), (3*Sqrt[-2 + x^2])/(2*Sqrt)

Maybe Mathematica 11 cannot solve for this problem, but why does it provide x-dependent eigenvalues?

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## My website gives “everybody” an error but it works just fine

I have website which runs just fine. I'm visiting it on PC, mobile, tablet and I'm even using Google Search Console & Analytics. And it just runs OK 100%. No issues whatsoever for me.

But when I'm promoting it (like direct Emails, social media etc.) I'm quite regularly getting responses "that website doesn't work" or "that link gives me an error". This issue lasts for months. I checked it on all my devices. I tried online web tests. Checked blacklists. Everything is OK. But…

My website gives "everybody" an error but it works just fine

## Axis Mapping gives one-sided values

this has got me stuck badly: my project is in 2.5D. Jumping and crouching not implemented yet.

Making use of Axis Mapping Input from the project settings, where numpad 4= 1 and numpad 6= -1 to control my movement, the follow problem poses itself:

I have a blendspace with a horizontal axis which is MovementDirection from -1 to 1 divided in 2.The upward axis is a MovementSpeed from 0 to = 200 = Max Walk Speed on my CharacterMovement asset.

In this Blendspace I go from idle in the bottom middle, to WalkForward and WalkBackward in the upper outer extremes.

However, when in my Level Blueprint I get my MovementSpeed and MovementDirection variables from my “BP_Player” Anim Instance, in order to print them, I can see that my MovementSpeed goes all the way to my max which is 200, while in the other direction it’s stuck around 0,01.

I thought it would go -200 but it doesn’t, which is messing up my WalkForward blendspace part, only blending very slightly into it.

However in the blendspace I have positioned my WalkForward and WalkBackward animations correctly.

Any idea where I could have gone wrong?

## i have this problem since i created the site, it gives me error 500 and 400 every time i publish a post!

Ho un grave problema sul mio sito Web ospitato su WordPress, ricevo l’errore 500 server e l’errore 404 invio un post e poi ricarico la pagina molte volte che l’errore scompare, e tutto torna alla normalità, ho guardato il registro di accesso e ho notato che al referar manca una lettera del mio sito che sarebbe sconti-coupon.it invece dice conti-coupon.it, dammi una mano per risolverlo per favore ..

In dndBeyond, I’m trying to essentially create a captain America shield. If I make it’s type a shield, then I can’t seem to make it give a ranged attack as an option. I’ve tried to add a modifier and used the Ranged Weapon Attack - Bludgeoning modifier with a damage die roll and dex as the primary stat. When equipped to a character the AC increases by 2 as it should for a shield, but no luck in getting a ranged attack to show up in the actions attack section of the character sheet. Can anyone give me some direction in how to make this happen? Does it need to be created as a weapon that gives an AC bonus to mimic what equipping a shield does? Kind of feels like a hack. 