How to make WordPress audio playlist understand the direct links of audio files shared on google drive?

this is my first post here and I excited! I used this approach to make a playlist with external links of audio files I have in my drive but unfortunately It couldn’t recognize the google drive direct link as a audio type file. Would you please guide me how I can solve this issue!?
Thank you in advance and sorry if my English is not well enough!

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calculus and analysis – Direct evaluation works but limit for the same points doesnt. Why?

p0(x_, a0_, b0_, a1_, b1_) := Piecewise({{1, 0 <= x <= 1}}, 0)
p1(x_, a0_, b0_, a1_, b1_) := Piecewise({{b0, 0 <= x <= 1 - a0}, {-(((1 - a0)*b0 - b1)/a0), 1 - a0 <= x <= 1 - a1}, {-(((1 - a0)*b0 - b1)/a0) - (-1 + b1)/a1, 1 - a1 <= x <= 1}}, 0)

a(y_, a0_?NumericQ, b0_?NumericQ, a1_?NumericQ, b1_?NumericQ) := Piecewise({{NIntegrate(p0(x, a0, b0, a1, b1), {x, 0, 1 - a0}), y == 0}, {NIntegrate(p0(x, a0, b0, a1, b1), {x, 1 - a0, 1 - a1}), y == 1}, {NIntegrate(p0(x, a0, b0, a1, b1), {x, 1 - a1, 1}), y == 2}}, 0)

b(y_, a0_?NumericQ, b0_?NumericQ, a1_?NumericQ, b1_?NumericQ) := Piecewise({{NIntegrate(p1(x, a0, b0, a1, b1), {x, 0, 1 - a0}), y == 0}, {NIntegrate(p1(x, a0, b0, a1, b1), {x, 1 - a0, 1 - a1}), y == 1}, {NIntegrate(p1(x, a0, b0, a1, b1), {x, 1 - a1, 1}), y == 2}}, 0)

aa(x_, a0_, b0_, a1_, b1_) := DiscreteConvolve(a(y, a0, b0, a1, b1), a(y, a0, b0, a1, b1), y, x)
bb(x_, a0_, b0_, a1_, b1_) := DiscreteConvolve(b(y, a0, b0, a1, b1), b(y, a0, b0, a1, b1), y, x)

fmyminquantize(a0_, b0_, a1_, b1_) := (1 - NSum(FullSimplify(Abs(bb(x, a0, b0, a1, b1) - aa(x, a0, b0, a1, b1))), {x, 0, Infinity})/2)/2

This works:

fmyminquantize(0.8, 0.2, 0.2, 0.4)

But this not.

fmyminquantize(a0, b0, a1, b1) /. {a0 -> 0.8, b0 -> 0.2, a1 -> 0.2, b1 -> 0.6}

Why? and how can one make it faster? because it is very very slow..

ag.algebraic geometry – Higher direct images of $mathbb{G}_m$ under a projective bundle

Let $X$ be a smooth projective rational variety over $mathbb{C}$, and let $pi:Yrightarrow X$ be a principal projective bundle with fibers isomorphic to $SL(n,mathbb{C})/P$, where $P$ is a parabolic subgroup. Consider the sheaf $mathbb{G}_m$ on $Y$ in e’tale topology.

I’m mainly interested in the cohomologies of the higher direct images. Can we describe the higher direct images $R^ipi_*(mathbb{G}_m)$ on $X$? For example, is $pi_*mathbb{G}_m$ a locally constant sheaf on $X$?

Any help would be appreciated.

perverse sheaves – Decomposition of direct image of a smooth morphism, Deligne’s theorem, motives

Let $f : X to Y$ be projective and smooth morphism of complex algebraic varieties. Here we care about the algebraic topology of $X$ and $Y$, so use classical topology for simplicity.

I can take the constant sheaf $mathbb{Q}_X$ and (derived) push it forward to get $f_* mathbb{Q}_X in D^b_c(Y,mathbb{Q})$. There is a celebrated theorem of Deligne that $f_* mathbb{Q}_X$ is semi-simple, i.e. isomorphic to a direct sum of its cohomology sheaves. The argument uses hard Lefschetz along the fibres. (It is also true that each summand is a semi-simple local system, as a polarizable VHS, however I want to ignore that extra piece of information below.)

Suppose I replace $mathbb{Q}$ with $k := mathbb{F}_p$.

Question: Is it true that $f_* k_X in D^b_c(Y,k)$ is always semi-simple? That is, does it always split as a direct sum of its (not-necessarily semi-simple) cohomology sheaves.

I had always assumed the answer was no, but woke up this morning feeling unusually optimistic. (I have tried several times to produce a counter-example.) I understand that this is deep water, and I am happy with a heuristic answer either way (potentially using motives).

ag.algebraic geometry – Can a Chow motif be isomorphic to its own direct summand?

Let $M$ be a $R$-linear Chow motif over a field $k$ that is perfect but not necessarily algebraically closed. Can one prove that $M$ is not a direct summand of itself (that is, $Mnotcong Mbigoplus N$ for every non-zero Chow motif $N$ over $k$)?

Is this statement clear for any particular $(k,R)$ (let us assume that the exponential characteristic of $k$ is invertible in $R$)? Do there exist any counterexamples (for torsion coefficients, probably)?

usability – What are the best practices to design user interfaces that are going to be used under direct sunlight?

Without having previous experience in this regard, if this were a personal project I would consider some logical aspects in terms of graphic elements. Regarding colors it’s obvious there must be a maximum contrast, so I only refer to the type of colors to choose.

1 – Avoid large white or light surfaces

It’s widely known that in optics a white surface reflects all the components of light while the black one absorbs. A wide white surface on the screen would be a total light reflection.


Image source

2 – Avoid 100% pure black

Especially on large surfaces.

By absorbing the 100% of the light, the black color can be transformed into a mirror. Although the reflection of an object (or the user) cannot be avoided, what can be done is to hide or disguise this reflection by the chosen color of the screen. For example using very low value colors, close to black, normally called off-black colors (Wikipedia). In the color scheme of this answer, it would be any center color on the left columns:

broken blacks

3 – Avoid 100% pure white

Any option that prevents a 100% reflection of the light is valid, for example a high value gray, close to white or any color in the second or third right column of the broken color scheme mentioned above, also called off-white colors (Wikipedia).

One of the laws of the theory of color perception says that any color will appear lighter on a darker background. It’s not necessary to use white to show luminosity:


4 – Avoid pure tints or colors

In optics, pure inks absorb part of the light components but reflect 100% of its color:


Personally I would replace them with colors that don’t contain 100% purity or saturation.


5 – Reduce graphic details

If possible, specially in all interactive elements. If the user see the interface on a screen under direct light, they will never see the small details of an object to be used, so they are totally unnecessary, they only cause noise.


6 – Avoid noise in general

The previous point also affects the rest of the interface components. The user will search for the information and interactivity elements, so any object or detail outside of these two functionalities is noise and can affect the immediate perception under the light.


7 – Prioritize Display Fonts

Regarding typography, I would not include so strict rules such as serif or sans serif. If the company commissioning the work uses serif fonts in all of its applications, the designer should abstain from this guideline. But I would give priority to Display fonts.

Within the types of font families, there is a classification regarding thickness based on size, these are the Display Fonts, whose highly exaggerated components allow an immediate visual perception.

This is the Display Fonts link from

In case of not being able to choose any typeface family outside of the corporate one, I would opt for variables of large size or pronounced thickness: minimum regular or semi-bold.

8 – Reduce visible length of information text

Interactivity offers very useful tools to avoid large information text in small size. A window with a clearly visible scrollbar and medium/big font size is preferable to not being able to read a whole very small text.

9 – Use area zooms

Personally, when using screen applications, I feel frustrated when I have to bring my head closer to see the content of certain elements in detail. I would not hesitate to use area zooms to highlight important elements such as text info or images, as happens in e-commerce with product’s cards.

10 – Optimize spacing

The question mentions three related elements:

  • Minimum font size
  • Spacing between items
  • Minimum item sizes

There is a common generic denominator in these three points: optimizing space. In graphic design there are virtual components that are also part of the composition set:

  1. Container frame
  2. Spaces and margins
  3. Structural diagramming lines

Knowing how to use them is related to the good disposition of all the other components (typography, text, images, animations, illustrations, etc). I don’t think there’s an immediate answer about an optimal use of these three components, they are influenced by the type of object to be made, the content and the receiver.

In this particular case, I would give priority to the interaction elements (buttons, scrollbars, zooms), avoid noise (described in previous points), try to group elements with similar functionalities, minimize information elements with possible zoom access.

In these two example images, the area for the buttons is the same height:


Well, sure there are so many more points to consider, but those are the ones that come to mind in a first instance analysis

algorithms – Implement a dictionary by using direct addressing on a huge array

algorithms – Implement a dictionary by using direct addressing on a huge array – Computer Science Stack Exchange

kubernetes – Kubernates CoreDNS direct a public url to a internal server

I have an app running in Kubernetes clusters which is accessing to a public api url for e.g. The app is accessing it within its code itself

I want to resolve that public url to an internal ip like how we can do it in /etc/host i.e. an entry like where that ip belong to one of our internal servers. This is for me to see the payload sent out and some internal checks

Can I do this via the CoreDNS?

I did it like this but does not seems to work

Corefile: |-
    .:53 {
        kubernetes cluster.local. {
            pods insecure
        hosts {
        prometheus :9153
        forward . /etc/resolv.conf
        cache 30

Is this the correct way to resolve a public url to an internal ip within Kubernetes?

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