What are some Google Keyword Planner alternative tools? – SEO Help (General Chat)

There are various sources to find alternative keywords tools. I have some:

Online: Here are some popular: KWFinder, Ahrefs, Moz, SEMRush, Ubersuggest and so on. These tools are easy to use. Some paid Ahrefs, SEMRush, Ubersuggest and some free Google Keyword Planner, KWFinder

Is it worth paying for guest posts with backlinks on high authority sites? – SEO Help (General Chat)

See, paying for guest posting sites is the assurity that the blogger will not remove your website link. It remains constant or live till the life of the website.
Publish the post on the best target blog, with high page rankings, from where you can expect to get a lot of genuine traffic. An imperative part of guest blogging is increasing traffic to your site.
This connection will send quality traffic to your site after somebody reads your blog post. An increase in site traffic implies more Visitors are going to your site to find out about your Services

general topology – When is a P-space the set of P-points of a compact Hausdorff space?

Let $X$ be a Hausdorff space. A point $xin X$ is a P-point if every countable intersection of open neighbourhoods of $x$ is open, and $X$ is a
P-space if every point is P-point, equivalently if every countable intersection of open sets is open.

The set of P-points in a compact Hausdorff space is thus a completely regular P-space. My question is: is every completely regular P-space equal to the set of P-points of some compact Hausdorff space?

If not, is there a characterisation of those completely regular P-spaces which are equal to the set of P-points of some compact Hausdorff space?

Example: a countable discrete set $N$ is a P-space and is equal to the set of P-points of its one-point compactification $Ncup{infty}$.

What are the best Forex trading platforms/brokers? – General Forex Questions & Help

Forex brokers are firms that provide currency traders with access to a trading platform that allows you to buy and sell foreign currencies. Retail forex brokers, handle a very small portion of the volume of the overall foreign exchange market.

Some of the best forex brokers:

Saxo Bank

This is considered one of the best forex brokers overall. It is the best overall because it has great competitive pricing to get involved, and has access to a wide range of markets. In addition it is very secure with multiple regulatory licenses. It also offers all forex traders with innovative trading platforms that really create more options for traders making them more successful.

Btw, I am trying to build a team with people who are interesting in learning how to trade. Here is the link to join my team and the name of the company is called mastery im academy. it is an education platform to learn how to trade https://iM.Academy/corp/cjoin?enroller=trade2bewealthy


This forex broker is considered best for CFD trades which means Contract For Difference. A contract for difference (CFD) is a popular form of trading that helps traders to speculate on the rising or falling prices of fast-moving global financial markets. This means that traders who like this trading style look for a wide range of tradable products in their platform which you can find globally on IG. IG is also very trusted around the world which is good for traders because they need to be able to trust their forex broker. They also provide Comprehensive research tools and real-time exchange data. In addition, they have a broad range of markets, including multi asset CFDs like cryptocurrencies.

TD AmeriTrade

This forex broker is only for US residents but it is great for Americans if you need a forex broker. If you are an American I would suggest this one because it is ranked number one for customer service and is very well trusted. It is regulated within the United States standards and is very heavily looked after. It has a wide array of premium research and tools to help traders succeed. They are predicted to start using Bitcoin trading which is also up to date and will be useful. They also have excellent phone support which can be an essential aspect of trading if you are hands on with questions and need answers.

Overall, these are some of the best forex trading brokers. I highly recommend taking a look at these three forex brokers because they are some of the most regulated and also have good tools.

What are the best ways to do content marketing? – SEO Help (General Chat)

Here are 9 ways to make your content marketing more effective:

·         Have a plan. …

·         Know your audience. …

·         Know when and where to post. …

·         Quality over quantity. …

·         Mix up content. …

·         Experiment. …

·         Focus on people, not search engines. …

·         Optimize your content.


general topology – A Set Theory of proving subset

Let $f: Xto Y$, and set $mathcal C$ which is not empty subsets of $X$, and a set $mathcal D$: $$emptysetneqmathcal Dsubseteqlbrace Binmathcal P(Y)midexists Ainmathcal C(B = f(A))rbrace.$$ Determine whether $$lbrace yin Ymidforall Ainmathcal C(yin f(A))rbracesubseteqbigcapmathcal D.$$

My understanding:
The set B in the first equation is different due to set f(A) mapped from different A. This means we can rewrite it as D∈{B1, B2, B3…}. Then we make an intersection of it, the result of which is the set mapped from every A∈C. Is that correct?
In the end, we have to show A⋂B=B or A⋃B=B to prove a subset. But I am lost in this step.Thank you in advance!

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Duda general Java Spring con HTML

Les comento: llevo tiempo queriendo montar un ERP que funcione en web, y me he fijado en Java Spring, dado que tengo alguna experiencia con Java, pero dado que es un framework que no he trabajado mucho, tengo algunas preguntas:

  • Es posible usar Spring Boot con Html/CSS de forma en que yo haga todo el diseño de la web con estos lenguajes y la parte programación la haga con Spring? Básicamente quiero hacer una web simple con las facilidades que da java, sobre todo en temas de gráficos (Canvas) y de informes (jasperreports).

  • En mi mente todo encaja porque en teoría es java, pero no sé si tendré problemas a la hora de controlar cuando hago click en un botón html para llamar por ejemplo a una función en java normal que por ejemplo me pinte un gráfico.

Básicamente quiero saber si con Java Spring podré hacer lo que pido, o es una ida de olla y tal vez debería decantarme por montar el ERP en Desktop.


generalized function – How do I make a general solver for a system of equations (e.g. thermodynamic processes) with different inputs and outputs?

Define Function(s) to Retrieve System of Equations

Rval=QuantityMagnitude@UnitConvert@Quantity(1, "MolarGasConstant");
idealGasEqn := Module({R=Rval,eqns}, eqns = {P*V == n*R*T})

Known Variables

Case 1: P, V, and n are knowns (Solve for T)

Pval1 = Quantity(1.5, "Atmospheres");
Vval1 = Quantity(3, "Liters");
nval1 = Quantity(1, "Moles");

Case 2: V, T, and n are knowns (Solve for P)

Vval2 = Quantity(3, "Liters");
nval2 = Quantity(1, "Moles");
Tval2 = Quantity(55,"Kelvins");



Equations, solve variables, and inputs

  • get system of equations based on input argument (e.g. type = “IdealGas”) using a Switch statement.
  • define list of solve variables (Symbols that are left unassigned)
  • define list of input variables (mixture of unassigned and assigned)


  • Get output unit and SI unit Quantities both with magnitude 1
  • find positions in solve variable and input lists based on variable type (Symbol or Quantity) using Position
  • replace quantities with magnitude of SI-converted quantities


  • solve for unknowns using SI magnitudes, no units in output (i.e. unitless) using Solve
  • attach SI magnitudes to unitless solution and convert to output units


  • output a unitless or unit-containing solution


idealGasSolver(P1_,V1_,n1_,T1_,type_:"IdealGas",unitlessQ_:False) := 
(*get system of equations*)
eqns = Switch(type,"IdealGas",idealGasEqn);

vars = {P,V,n,T}; (*Symbols for solve, keep unassigned throughout*)
valsTmp = {P1,V1,n1,T1}; (*input values, some are Symbols, some are Quantities*)

(*units with magnitude 1*)
outUnits = Quantity(1,#)&/@{"Atmospheres","Liters","Moles","DegreesCelsius"};
SIunits = Quantity(1,#)&/@QuantityUnit@UnitConvert@outUnits;

(*find positions based on variable type*)
getIDs(head_) := Position(Head@#===head&/@valsTmp,True)//Flatten;
quantityIDs = getIDs(Quantity);
symbolIDs = getIDs(Symbol);

(*replace quantities with magnitude of SI - converted quantities*)
rules1 = MapThread(#1->#2&, 
vals = ReplacePart(valsTmp,rules1);

(*solve for unknowns using SI magnitudes, no units in output*)
rules2 = MapThread(#1->#2&,{vars((quantityIDs)),vals((quantityIDs))});
unitlessSoln = Solve(eqns/.rules2,vars((symbolIDs)))((1));

(*convert solution to output units and include units*)
rules3 = MapThread(#1 -> #2 &, {vars((symbolIDs)), 
outVals = MapThread(UnitConvert(#1,#2)&, 
unitSoln = MapThread(#1->#2&,{vals((symbolIDs)),outVals});

(*output a solution based on unitlessQ argument*)
outsoln = If(unitlessQ,unitlessSoln,unitSoln)

Case 1

Make sure that temperature input is unassigned and specifically use the variable “T”.

idealGasSolver(Pval1, Vval1, nval1, T) (*output in units based on outUnits (deg C)*)
idealGasSolver(Pval1, Vval1, nval1, T, "IdealGas", True) (*output temperature SI unit (K) magnitude*)

{T -> Quantity(-218.31031631383098, "DegreesCelsius")}
{T -> 54.83968368616898}

We get units with the first output, and an SI magnitude with the second.

Case 2

Make sure that pressure input is unassigned and specifically use the variable “P”.

idealGasSolver(P, Vval2, nval2, Tval2) (*output in units based on outUnits (atm)*)
idealGasSolver(P, Vval2, nval2, Tval2, "IdealGas", True) (*output pressure SI unit (Pa) magnitude*)

{P -> Quantity(2286477219992141/1519875000000000, "Atmospheres")}
{P -> 2286477219992141/15000000000}

Exact arithmetic is preserved in this case.

Case 3 (additional case, underdetermined system of equations)

Make sure that all inputs except temperature are unassigned and specifically use the variables “P”, “V”, and “n”.

Clear(P, V, n)
idealGasSolver(P, V, n, Tval2) // N
idealGasSolver(P, V, n, Tval2, "IdealGas", True) // N (*output SI magnitude*)

{P -> UnitConvert(P*Quantity(1., "Kilograms"/("Meters"*"Seconds"^2)), Quantity(1., "Atmospheres")), V -> UnitConvert(V*Quantity(1., "Meters"^3), Quantity(1., "Liters")), n -> UnitConvert(P*V*Quantity(0.002186770091685928, "Moles"), Quantity(1., "Moles"))}
{n -> 0.002186770091685928*P*V}

The second output (SI magnitude) is more parsable and less subject to issues if you were to apply this process successively (i.e. use the outputs as inputs to the next system of equations).

general topology – Yes/No : Is the subspace $A times { b }$ of $A times B$ is homeomorphic to $A$?

Yes/No : Is the subspace $A times { b }$ of $A times B$ is homeomorphic to $A$?

My attempt : No

Here if we remove one point from $A times { b }$ then $(A times { b }) setminus{1}$ is connected since $mathbb{R}^n$ is connected if $n >1$

But if we remove one point from $A$ then $A setminus {1}$ is not connected

so $A times { b } notcong A$