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# Travelling Wave Line Model

## Introduction

Figure 1. Travelling wave along a line (image courtesy of Wikipedia)

A travelling wave on a transmission line is a transient disturbance that that moves along the line at a constant speed yet maintains its shape (see Figure 1). Examples include lightning surges, switching transients, faults, etc.

In this article, we will derive various time-domain models for travelling waves on transmission lines, starting from the simplest case of the lossless single-phase line, then building to a generic lossy single-phase line. The derivation of the model is also looked at starting from the frequency-domain, showing the symmetry of the frequency and time-domain models. Finally, the considerations required to extend the model to a multi-conductor line is discussed.

This article provides the theoretical background for the travelling wave model. Actual implementations of the model suitable for use in computer simulations (i.e. discrete-time) can be found in the following articles:

## Lossless Single-Phase Lines

Figure 2. Travelling wave line model - Small Segment from a lossless single-phase line

Consider the small segment of length $\Delta x$ metres from a lossless single-phase transmission line shown in Figure 2.

Notice that the model is similar to that of the classical distributed parameter line model, except that in this model, the voltages and currents are functions of both distance $x$ and time $t$ and are real, not phasor quantities. In the classical distributed parameter line model, the voltages and currents are evaluated at steady-state and are only functions of distance $x$.

### Derivation of Voltage and Current Equations

Analysing this circuit using Kirchhoff's voltage law and Kirchhoff's current law, we can get the following pair of equations:

$V(x + \Delta x, t) = V(x,t) - L \Delta x \frac{\partial I(x + \Delta x,t)}{\partial t} \,$
$I(x,t) = I(x + \Delta x, t) + C \Delta x \frac{\partial V(x,t)}{\partial t} \,$

Notes:

1. The voltage across an inductor is $v = L \frac{di}{dt}$ and the current through a capacitor is $i = C \frac{dv}{dt}$.
2. Partial derivatives are used because the voltages and currents are functions of both time and distance.

Re-arranging the above equations, we get:

$\frac{V(x + \Delta x, t) - V(x,t)}{\Delta x} = - L \frac{\partial I(x + \Delta x,t)}{\partial t} \,$
$\frac{I(x + \Delta x, t) - I(x,t)}{\Delta x} = - C \frac{\partial V(x,t)}{\partial t} \,$

Taking the limit as $\Delta x \to 0 \,$ yields the well known Telegrapher's equations:

$\frac{\partial V(x, t)}{\partial x} = - L \frac{\partial I(x,t)}{\partial t} \,$ ... Equ. (1)
$\frac{\partial I(x,t)}{\partial x} = - C \frac{\partial V(x,t)}{\partial t} \,$ ... Equ. (2)

Differentiating the voltage equation with respect to x and the current equation with respect to t:

$\frac{\partial^{2} V(x, t)}{\partial x^{2}} = - L \frac{\partial^{2} I(x,t)}{\partial x \partial t} \,$ ... Equ. (3)
$\frac{\partial^{2} I(x,t)}{\partial x \partial t} = - C \frac{\partial^{2} V(x,t)}{\partial t^{2}} \,$ ... Equ. (4)

Now substituting Equ. (4) into Equ. (3), we get:

$\frac{\partial^{2} V(x, t)}{\partial x^{2}} = LC \frac{\partial^{2} V(x,t)}{\partial t^{2}} \,$ ... Equ. (5)

Similarly, we could have differentiated the current equation with respect to x and the voltage equation with respect to t and then solved for the current equation:

$\frac{\partial^{2} I(x, t)}{\partial x^{2}} = LC \frac{\partial^{2} I(x,t)}{\partial t^{2}} \,$ ... Equ. (6)

The pair of equations (5) and (6) above are referred to as the transmission line wave equations.

The general solution to either of these equations can be found using d'Alembert's formula:

$I(x, t) = i^{+}(x - vt) + i^{-}(x + vt) \,$
$V(x, t) = v^{+}(x - vt) + v^{-}(x + vt) \,$

where $v = \frac{1}{\sqrt{LC}} \,$ is the velocity of propagation (m/s).

$i^{+}(t) \,$ and $i^{-}(t) \,$ are arbitrary current functions of time.
$v^{+}(t) \,$ and $v^{-}(t) \,$ are arbitrary voltage functions of time.

Using the current equation above, we can solve for the voltage equation as follows (see here for the full derivation):

$v(x, t) = Z_{c} \left[ i^{+}(x - vt) - i^{-}(x+vt) \right] \,$

where $Z_{c} = \frac{1}{vC} = \frac{\sqrt{LC}}{C} = \sqrt{\frac{L}{C}}$ is the characteristic impedance (Ohms)

### Significance of + and - Equations

So we have the pair of voltage and current equations:

$I(x, t) = i^{+}(x - vt) + i^{-}(x + vt) \,$
$V(x, t) = Z_{c} \left[ i^{+}(x - vt) - i^{-}(x+vt) \right] \,$

What is the significance of $i^{+}(x - vt) \,$ and $i^{-}(x + vt) \,$?

Consider that time t=0s, the function $i^{+}(x) \,$ represents an arbitrary waveform / shape distributed in space along the transmission line. For example, it could look like this:

Figure 3. Arbitrary waveform $i^{+}(x)$ at time t = 0s

Now consider what happens at time t=1s, the function $i^{+}(x - v) \,$ has the same shape as the function above, but is translated to the right by $v \,$ metres:

Figure 4. Arbitrary waveform $i^{+}(x - v)$ at time t = 1s

What we can conclude is that the function $i^{+}(x - vt) \,$ is an arbitrary waveform that maintains its shape but moves in the direction of the receiving end with increasing time at speed $v \,$ m/s. This is called a forward travelling wave.

We can use similar logic to conclude that the function $i^{-}(x + vt) \,$ is an arbitrary waveform that moves in the opposite direction (i.e. in the direction of the sending end). This is referred to as a backward travelling wave.

## Generic Lossy Single-Phase Lines

Figure 5. A generic single-phase distributed parameter line model

Consider the generic single-phase distributed parameter line model of length $l \,$ metres shown in Figure 5. Analysing the circuit using Kirchhoff's laws as we did previously in the lossless case, we can get:

$\frac{\partial V(x, t)}{\partial x} = - I(x,t) R - L \frac{\partial I(x,t)}{\partial t} \,$
$\frac{\partial I(x,t)}{\partial x} = -V(x,t) G - C \frac{\partial V(x,t)}{\partial t} \,$

Where $G = \frac{1}{R_{sh}} \,$ is the shunt conductance.

Differentiating the voltage equation with respect to x and the current equation with respect to t:

$\frac{\partial^{2} V(x, t)}{\partial x^{2}} = - R \frac{\partial I(x,t)}{\partial x} - L \frac{\partial^{2} I(x,t)}{\partial x \partial t} \,$ ... Equ. (7)
$\frac{\partial^{2} I(x,t)}{\partial x \partial t} = - G \frac{\partial V(x,t)}{\partial t} - C \frac{\partial^{2} V(x,t)}{\partial t^{2}} \,$ ... Equ. (8)

Substituting Equ. (8) into Equ. (7), we get:

$\frac{\partial^{2} V(x, t)}{\partial x^{2}} = - R \frac{\partial I(x,t)}{\partial x} + LG \frac{\partial V(x,t)}{\partial t} + LC \frac{\partial^{2} V(x,t)}{\partial t^{2}} \,$ ... Equ. (9)

If we were to set R = G = 0 in the equation above, then we would get the same transmission line wave equation as Equ. (5) in the lossless case.

However, while there is a general solution to the lossless line using d'Alembert's formula (as shown earlier), the generic lossy line does not have a neat, closed-form solution.

## Frequency Domain Derivation

In the preceding sections, the travelling wave model was developed purely in the time-domain. Another way of looking at the travelling wave model is to derive it first in the frequency domain and then convert it to the time-domain. Recall from the steady-state (frequency domain) distributed parameter model that the sending end voltage and current can be related to the receiving end quantities as follows:

$\left[ \begin{matrix} \boldsymbol{V_{s}} \\ \\ \boldsymbol{I_{s}} \end{matrix} \right] = \left[ \begin{matrix} \cosh (\boldsymbol{\gamma} l) & \boldsymbol{Z}_{c} \sinh(\boldsymbol{\gamma} l) \\ \\ \frac{1}{\boldsymbol{Z}_{c}} sinh (\boldsymbol{\gamma} l) & \cosh(\boldsymbol{\gamma} l) \end{matrix} \right] \left[ \begin{matrix} \boldsymbol{V_{r}} \\ \\ \boldsymbol{I_{r}} \end{matrix} \right] \,$

where $\boldsymbol{\gamma} = \sqrt{\boldsymbol{zy}}$ is the propagation constant ($m^{-1}$)

$\boldsymbol{Z}_{c} = \sqrt{\boldsymbol{\frac{z}{y}}}$ is the characteristic impedance ($\Omega$)
$\boldsymbol{z} = R + j \omega l$ and $\boldsymbol{y} = G + j \omega C$ are the series impedance and shunt admittance respectively

With some straightforward algebraic manipulation, the steady-state equations above can be represented in the following form:

$\boldsymbol{V_{r}} + \boldsymbol{Z}_{c} \boldsymbol{I_{r}} = (\boldsymbol{V_{s}} + \boldsymbol{Z}_{c} \boldsymbol{I_{s}}) e^{-\boldsymbol{\gamma} l}$ ... Equ. (10)

The time-domain model can be derived by calculating the inverse Fourier transform of Equ. (10).

In the lossless case (i.e. R = G = 0.), the propagation constant and characteristic impedance are as follows:

$\boldsymbol{\gamma} = \sqrt{\boldsymbol{zy}} = \sqrt{(j \omega L)(j \omega C)} = j \omega \sqrt{LC}$
$\boldsymbol{Z}_{c} = \sqrt{\boldsymbol{\frac{z}{y}}} = \sqrt{\frac{(j \omega L)}{(j \omega C)}} = \sqrt{\frac{L}{C}}$

A property of Fourier transforms is that multiplying by a complex exponential in the frequency domain results in a time shift in the time domain. Therefore, taking the inverse Fourier transform of Equ. (10) for the lossless case, we get:

$v_{r}(t) + \sqrt{\frac{L}{C}} i_{r}(t) = v_{s}(t - \sqrt{LC} l) + \sqrt{\frac{L}{C}} i_{s}(t - \sqrt{LC} l) \,$

The lossless case above shows that the receiving end quantities are essentially time-shifted (past) versions of the sending end quantities, as was derived earlier using d'Alembert's formula.

In the general lossy case, the characteristic impedance is not a scalar constant (but rather a function of frequency $\boldsymbol{Z}_{c}(\omega) \,$) and the propagation constant does not lead to a simple time shift in the time-domain. Therefore, the inverse Fourier transform of Equ. (10) leads to a series of messy convolutions:

$v_{r}(t) + z_{c}(t) * i_{r}(t) = \left[ v_{s}(t) + z_{c}(t) * i_{s}(t) \right] * a(t) \,$

where $a(t) \,$ is the inverse Fourier transform of $e^{-\boldsymbol{\gamma}(\omega) l} \,$

$z_{c}(t) \,$ is the inverse Fourier transform of $\boldsymbol{Z}_{c}(\omega) \,$

As can be imagined, the convolution integrals in the equation above are not neatly solvable.

## Multi-conductor Lines

The travelling wave line model for the single-phase lossless line can be extended to a multi-conductor line of n conductors by replacing the voltage and current quantities with $n \times 1$ vectors, e.g. for a three-phase, three-conductor line:

$\boldsymbol{V}(x,t) = \left[ \begin{matrix} \boldsymbol{V_{a}}(x,t) \\ \boldsymbol{V_{b}}(x,t) \\ \boldsymbol{V_{c}}(x,t) \end{matrix} \right] \,$, $\boldsymbol{I}(x,t) = \left[ \begin{matrix} \boldsymbol{I_{a}}(x,t) \\ \boldsymbol{I_{b}}(x,t) \\ \boldsymbol{I_{c}}(x,t) \end{matrix} \right] \,$

And the inductance and capacitance (per unit length) with $n \times n$ matrices to capture the mutual coupling between phases, e.g. for a three-phase, three-conductor line:

$[L] = \left[ \begin{matrix} L_{aa} & L_{ab} & L_{ac} \\ L_{ba} & L_{bb} & L_{bc} \\ L_{ca} & L_{cb} & L_{cc} \end{matrix} \right] \,$
$[C] = \left[ \begin{matrix} C_{aa} & C_{ab} & C_{ac} \\ C_{ba} & C_{bb} & C_{bc} \\ C_{ca} & C_{cb} & C_{cc} \end{matrix} \right] \,$

The transmission line wave equations for the single-phase model (see equations (5) and (6) above) can now be re-written for the multi-conductor model as follows:

$\frac{\partial^{2} \boldsymbol{V}(x, t)}{\partial x^{2}} = [L][C] \frac{\partial^{2} \boldsymbol{V}(x,t)}{\partial t^{2}} \,$ ... Equ. (10)
$\frac{\partial^{2} \boldsymbol{I}(x, t)}{\partial x^{2}} = [C][L] \frac{\partial^{2} \boldsymbol{I}(x,t)}{\partial t^{2}} \,$ ... Equ. (11)

Unlike the single-phase case, there is no general solution to the second-order differential equations (10) and (11) since the matrix product [L][C] is typically full (i.e. off-diagonals are non-zero). To solve these differential equations, a modal transformation is required to decouple the phases (refer to this section of the distributed parameter line article for more details on the modal transformation).

The voltage and current vectors are transformed from the phase domain to the modal domain by the $n \times n$ transformation matrices $[T_{v}] \,$ and $[T_{i}] \,$, such that:

$\boldsymbol{V}(x,t) = [T_{v}] \boldsymbol{V'}(x,t)$
$\boldsymbol{I}(x,t) = [T_{i}] \boldsymbol{I'}(x,t)$

where $\boldsymbol{V'}(x,t)$ and $\boldsymbol{I'}(x,t)$ are the modal voltage and current vectors, i.e.

$\boldsymbol{V'}(x,t) = \left[ \begin{matrix} \boldsymbol{V_{0}}(x) \\ \boldsymbol{V_{1}}(x) \\ \boldsymbol{V_{2}}(x) \end{matrix} \right] \,$, $\boldsymbol{I'}(x,t) = \left[ \begin{matrix} \boldsymbol{I_{0}}(x) \\ \boldsymbol{I_{1}}(x) \\ \boldsymbol{I_{2}}(x) \end{matrix} \right] \,$

The transformation matrices $[T_{v}] \,$ and $[T_{i}] \,$ are selected such that they are the eigenvectors of [L][C] and [C][L] respectively (note that they have the same eigenvalues).

In the modal domain, equations (10) and (11) can be re-written as sets of decoupled equations, i.e.

$\left[ \begin{matrix} \frac{d^{2} \boldsymbol{V_{0}}(x,t)}{dx^{2}} \\ \\ \frac{d^{2} \boldsymbol{V_{1}}(x,t)}{dx^{2}} \\ \\ \frac{d^{2}\boldsymbol{V_{2}}(x,t)}{dx^{2}} \end{matrix} \right] = \left[ \begin{matrix} \lambda_{0} & & \\ & \lambda_{1} & \\ & & \lambda_{2} \end{matrix} \right] \left[ \begin{matrix} \frac{d^{2} \boldsymbol{V_{0}}(x,t)}{dt^{2}} \\ \\ \frac{d^{2} \boldsymbol{V_{1}}(x,t)}{dt^{2}} \\ \\ \frac{d^{2}\boldsymbol{V_{2}}(x,t)}{dt^{2}} \end{matrix} \right] \,$ ... Equ. (12)
$\left[ \begin{matrix} \frac{d^{2} \boldsymbol{I_{0}}(x,t)}{dx^{2}} \\ \\ \frac{d^{2} \boldsymbol{I_{1}}(x,t)}{dx^{2}} \\ \\ \frac{d^{2}\boldsymbol{I_{2}}(x,t)}{dx^{2}} \end{matrix} \right] = \left[ \begin{matrix} \lambda_{0} & & \\ & \lambda_{1} & \\ & & \lambda_{2} \end{matrix} \right] \left[ \begin{matrix} \frac{d^{2} \boldsymbol{I_{0}}(x,t)}{dt^{2}} \\ \\ \frac{d^{2} \boldsymbol{I_{1}}(x,t)}{dt^{2}} \\ \\ \frac{d^{2}\boldsymbol{I_{2}}(x,t)}{dt^{2}} \end{matrix} \right] \,$ ... Equ. (13)

These modal differential equations can then be solved individually using d'Alembert's formula. For example, the solution for mode 0 is:

$I_{0}(x, t) = i_{0}^{+}(x - v_{0}t) + i_{0}^{-}(x + v_{0}t) \,$
$V_{0}(x, t) = v_{0}^{+}(x - v_{0}t) + v_{0}^{-}(x + v_{0}t) \,$

where $v_{0} = \frac{1}{\sqrt{\lambda_0}} \,$ is the velocity of propagation for mode 0 (m/s)

$i^{+}(t) \,$ and $i^{-}(t) \,$ are current functions for mode 0
$v^{+}(t) \,$ and $v^{-}(t) \,$ are voltage functions for mode 0

Once modal domain quantities are calculated, then the phase domain quantities can be found by applying the inverse transformation.

Finally, it should be noted that the general solution using the modal transformation only applies to lossless multi-conductor lines. The generic lossy line suffers from the same issues as described earlier for the lossy single-phase line, i.e. multiple cross-coupling terms that render d'Alembert's formula unusable.

## Frequency Dependency of Line Parameters

So far, we have described the per unit length inductance (L), capacitance (C), resistance (R) and conductance (G) parameters of the line as fixed and constant for the full range of frequencies. However, this is not a valid assumption, particularly at high frequencies. For example, the skin effect leads to higher resistances at higher frequencies. It is therefore more correct to characterise the line parameters as having frequency dependencies, i.e. $L(\omega) \,$, $C(\omega) \,$, $R(\omega) \,$ and $G(\omega) \,$.

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# Classification and properties of quantum spin liquids on the hyperhoneycomb lattice

Research paper by Biao Huang, Wonjune Choi, Yong Baek Kim, Yuan-Ming Lu

Indexed on: 12 Feb '18Published on: 12 Feb '18Published in: arXiv - Physics - Strongly Correlated Electrons

#### Abstract

The family of "Kitaev materials" provides an ideal platform to study quantum spin liquids and their neighboring magnetic orders. Motivated by the possibility of a quantum spin liquid ground state in pressurized hyperhoneycomb iridate $\beta$-Li$_2$IrO$_3$, we systematically classify and study symmetric quantum spin liquids on the hyperhoneycomb lattice, using the Abrikosov-fermion representation. Among the 176 symmetric $U(1)$ spin liquids (and 160 $Z_2$ spin liquids), we identify 8 "root" $U(1)$ spin liquids in proximity to the ground state of the solvable Kitave model on hyperhonecyomb lattices. These 8 states are promising candidates for possible $U(1)$ spin liquid ground states in pressurized $\beta$-Li$_2$IrO$_3$. We further discuss physical properties of these 8 $U(1)$ spin liquid candidates, and show that they all support nodal-line-shaped spinon Fermi surfaces.


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# trinity['s concept] exists in the bible

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Artur
 Voting Style: Open Point System: 7 Point Started: 2/3/2014 Category: Religion Updated: 3 years ago Status: Post Voting Period Viewed: 911 times Debate No: 45123
Debate Rounds (5)

 Con Hello everybody. I am going to start a new debate, about trinity.. triune god [of christians].The doctrine or concept of the Trinity is central to most Christian denominations and faith groups, although not all.DEFINITION:trinity: 1. Trinity Theology In most Christian faiths, the union of three divine persons, the Father, Son, and Holy Spirit, in one God. Also calledTrine. http://bit.ly...2. according to this definition of wikipedia, trinity is composed of the father, the son and the holy spirit. [if this picture is too small to be seen, you may visit this link: http://upload.wikimedia.org...]and according to the same definition, the father is god, the son is also god and the spirit is also god. [seen from picture]url adress:http://bit.ly...considering the definition given by wikipedia, I can say that: 3 of that 3 are god.for debate, I will ask my opponent to show us that the trinity or its concept exists in the bible. I ask him/her to show us verse[s] or references from the bible. PRO needs to show us verses/reference from the bible that: talks about the godness of the father. talks about the godness of the son. talks about the godness of the hole spirit. RULES:1. anybody can accept this debate but it would be better if my opponent is a christian who believes in triune god exists in the bible.2. forfeits are allowed, if one side forfeits he may answer on next round.3. when my opponent, PRO sets his arguements, number of arguements presented in one round must NOT be more than 5 so that I will have no character insufficiency. [if opponent violates this rule, I ask voters to keep it in mind.]4. no defamation, insulting or personal attack. [if any of us violates this, I ask voters to penalise him/her]5. since PRO will talk after me, he does not have to present new arguement[s] in th elast round.5 rounds, 8000 character. we have 72 hours to argue.no need to waste round for acceptance, PRO may start from first round. btw, I hope I didnot forget any rule or smth to write.bonus: there are so many rumours that "the quran permits/commands muslims to kill innocent people of nonmuslims". as a person who read the quran and not muslim, I can say that quran doesnot. if anybody wants to debate this, he may challenge, I will accept it. Report this Argument Pro (1) Jesus is called God, but since there is only one God, Jesus must be that one God or else he is a false God: The Scriptures proclaim that there is one, and only one God in all of existence. (Deu 4:35; Isa 43:10-11; 44:6, 8; 45:5-6, 14, 21-22; 46:9; Mal 2:10; Rom 3:30; 1 Cor 8:6; Eph 4:6; Jam 2:19) It also says that there is only one true God. (John 17:3; 1 John 5:20) This means that all other gods are false. Since there is only one God, then no other being can truly be a god. This is why they are false gods. Now, Scripture plainly identifies the Son as God in John 20:28. The term "my God" refers to the true God every other time it is used in the Bible, establishing the consistent linguistic use of the term. Thomas here calls Jesus in the Greek, ho kurious mou kai ho theos mou, literally, the Lord of me and the God of me. So John 20:28 calls Jesus the God of Thomas, and in verse 29 Jesus approves. Now since there is only one true God, either Jesus was the true God in John 20:28, or a false god. Which is it? I look forward to my opponents answer. But Jesus is also identified as God in Isaiah 9:6. So which is it: is he a true god, or a false god? If he is a true god, then he must be the Almighty, for there is only one true God, not two; if he is a false god, we are not saved, for no pretender could save us. I must at this point mention the Granville Sharp rule of Greek grammar. This rule states that when there are 2 nouns that are both singular which describe a person, and these nouns are connected by the word "and," the first noun having the article, the second noun not having the article then they refer to the SAME PERSON. (*Note that the nouns cannot be personal names*) There is absolutely no exception to this rule in all of the Greek New Testament. Having stated this rule I find it necessary to present two verses of scripture that unequivocally qualify Jesus as both God and Savior. Titus 2:13 - while we wait for the blessed hope"the glorious appearing of our great God and Savior, Jesus Christ, (NIV) 2Peter 1:1 - Simon Peter, a servant and apostle of Jesus Christ, To those who through the righteousness of our God and Savior Jesus Christ have received a faith as precious as ours: (NIV) Notice in both verses the noun "God" (theou) has the article (tou) and is connected to the second noun "Savior" (soteros) which does not have an article, by the word "and" (kai). Thus "God and Savior" both refer to the Person of Jesus. Grammatically this is irrefutable. So not only is Jesus Savior, He is God! So I think I have made a good case that Jesus is definitely God, and since there is only one God, then the Father and the Son must be one God. Now, onto the Holy Spirit. (2) There is only one Creator: the Father, Son and Holy Spirit: Isa 44:24 tells us that Yahweh made all things, streached out the heavens alone, spread out the earth by himself; yet Scripture reveals the Father as creator (Isa 64:8), and the Son (Col 1:16-17; Heb 1:2, 8-10), and the Holy Spirit (Ps 104:30; Job 26:13; 33:4) Combine this with the plural pronouns "us" and "our" in Genesis 1:16 and the trinitarian has an airtight case. If Jesus and the Holy Spirit are not one God with the Father, then God the Father had help and did not create all things alone, by himself, as he said in Isaiah 44:24. If the trinity is true, harmony comes to the texts. (3) God is the only Savior, so being the Savior means Jesus is God: At Isaiah 43:11 Yahweh declares, "I myself am Yahweh and besides me there is no Savior." (WEB) Scripture tells us plainly that Jesus is the Savior. (Matt 1:21; Lu 2:11; Acts 4:12; 2 Tim 1:10; Tit 1:4; 2 Pet 1:11, etc) So is Jesus Yahweh himself, or is he another Savior besides Yahweh? Which is it? If he is Yahweh, then he must be one Yahweh with the Father. For there is only one Yahweh. (Deu 6:4) If he is not Yahweh, then he is another savior besides Yahweh, and Yahweh was lying when he claimed to be the only Savior. Which is it? Acts 4:12 says of Jesus, that "there is no salvation in anyone else." Now, if Jesus is not God, then there can be no salvation in God, for there is no salvation in anyone else but Jesus. (4) The Holy Spirit has the attributes of God and is called God: That the Holy Spirt is God and Lord is clearly stated in the Scriptures. (Acts 5:3-4; 2 Cor 3:17) The Holy Spirit has the same attributes of diety as the Father and the Son: The Father is eternal (Ps 90:2), and the Son (Isa 9:6; Mic 5:2), and the Holy Spirit (Heb 9:14) The Father is omniscient (1 John 3:20), and the Son (John 16:30; 21:17), and the Holy Spirit (1 Cor 2:10-11) The Father is omnipresent (1 Kings 8:27; Ps 137:8-18), and the Son (Matt 18:20), and the Holy Spirit. (Ps 137:7) The Father is omnipotent (Dan 4:35), and the Son (Matt 28:18; John 17:10), and the Holy Spirit (Isa 40:12-18) (5) There is no one like God, but Jesus is just like God: In Isaiah 46:9 God says there is on one like him; but Jesus says if you have seen him, you have seen the Father, and Paul describes him as the image of God, and the impress image of his person. (John 14:6-9; Col 1:15; Hebrews 1:3) Summary: I have shown the deity or godhood of the Father, Son, and Holy Spirit from the Bible. I have also shown there is only one God from the Bible. Trinity proved.Report this Argument Con Thank you for your answers, the first thing I would like to say about the arguement of my opponent: seems that he misunderstood the challenge: I did not ask him to prove that Jesus or any other two is god. I asked him to give verses/references which talk about the deity of fatehr, god and spirit. in the first arguement of his, he brought verses about the godness of Jesus and asked me to reply, I do not need reply in this debate, since the debate is to show verses, not to clarify nor analyse them. RESPONSES:1. PRO showed me verses which talk about Jesus as god, I agree with him and I see no need to [try to] refute or answer him. so, with the first arguement of his, he completed 1/3 of the challenge: HE talked about the godness of the SON. remaining two. even me can give everal verses about JEsus a god from the epistles.____________________________________________________________________________________2. int he second arguement of HIS, PRO showed me[/us] verses which talk about the godness of the father the god.but he said: {yet Scripture reveals the Father as creator (Isa 64:8), and the Son (Col 1:16-17; Heb 1:2, 8-10), and the Holy Spirit (Ps 104:30; Job 26:13; 33:4) } since he showed us the verses about the godness of Jesus[/son] and Yahweh[/father] I see no need to talk about them, I am going to talk about the spirit here. [underlined part.]PRO gave this references: Ps 104:30; Job 26:13; 33:4Now, I am going to copy ps104:30 first: Psalm 104:30 New International Version (NIV) 30 When you send your Spirit, they are created, and you renew the face of the ground. http://www.biblegateway.com...this verse does not say unambiguously that the spirit is the creator. by using ambiguous interpretations this verse can be interpreted as "it says that the spirit is creator" but even PRO shows us that it says spirit is creator, then he does not complete the challenge for the godness of spirit, all he will do is to show that spirit is also creator, but the challenge is to show reference which talks about the godness of the spirit, not his creativity. and at the same time he will make one more contradiction to the bible [if this contradiction is not already discovered]the contradiction can be made by this interpretation is: is Yahweh the creator of all things by himself?Isaiah 44:24 says: yes, he created everything by himself. I am the Lord, the Maker of all things, who stretches out the heavens, who spreads out the earth by myselfthis verse says: no. there are somethings created by not Yahweh, spirit. When you send your Spirit, they are created, and you renew the face of the ground.job26:13By his breath the skies became fair; his hand pierced the gliding serpent. it does not say the spirit is creator.then, he said: {Combine this with the plural pronouns "us" and "our" in Genesis 1:16 and the trinitarian has an airtight case. }first of all, this is not plural of numbers, in semantic languages it is plural of degree/respect. I can speak 1 semiti language [but not hebrew], in languages like this, when you are talking with somebody and if you consider yourself as greater than him then instead of I "we" is used. For example:if I am a general of the army and you are an ordinary soldier, then when I am talking to you I will say: "Listen to us" instead of listen to me.but if my opponent is going to say "no, I do not accept this definition of yours" then that verse does not become triunity, triunity is one thing, but "us and our is for more than one." I can use that verse for "MONOTHEISM", for consistency, he needs to agree that christianity is monotheistic religion because in genesis1:16 god said "us and our" which means more than one gods. and monotheism is not trinity. in both ways, this does not become trinity.then my opponent said: {If Jesus and the Holy Spirit are not one God with the Father, then God the Father had help and did not create all things alone, by himself, as he said in Isaiah 44:24. If the trinity is true, harmony comes to the texts.} so, one more absurdity of the bible but I will talk about this part: so, the thing my opponent himslef showed us is not the godness of spirit, he showed us one more error of the bible. the thing he showed us is: In Isaiah44:24 the father says that he is the only creator {by saying: "by myself"}to correct it, PRO needs to show us where it is said that HOLY SPIRIT IS GOD, if he cant, then he will have shown us one more error of the bible.(3) with the third arguement of him, he again used some verses about the godness of jesus, I agree with him, when we look at the epistles from new testament we can read that in several places Jesus is written as god. since the aim of the is NOT to discuss/clarify/debate whetther is true or not, I dont need to refute or reply these, I say: PRO one more time completed the challenge for the godness of Jesus. [/son](4) in the 4th arguement of his my opponent said: {(4) The Holy Spirit has the attributes of God}Does it answer the challenge? no, it does not. having the same attrobute does not mean that that two are the same thing, since diffrent things may have the attribute of each other, it does not complete the challenge. and then he went on:{and is called God:} He is called GOD but by whom? and my opponent gave verses/references:{(Acts 5:3-4; 2 Cor 3:17} first, acts5:3-4: Peter said, “Ananias, how is it that Satan has so filled your heart that you have lied to the Holy Spirit and have kept for yourself some of the money you received for the land? 4 Didn’t it belong to you before it was sold? And after it was sold, wasn’t the money at your disposal? What made you think of doing such a thing? You have not lied just to human beings but to God.”it doesnot say "HOLY spirit is god", it can be interpreted in this way but at the same time it can be otherwise. if my Opponent can show us how it says spirit is god, I can interprete and show that it says otherwise.2cor2:17:Now the Lord is the Spirit, and where the Spirit of the Lord is, there is freedom.I hope we all know the diffrence between god and lord. but for the sake of debate:lord is generally used for persons who are of higher rank in society. Lord is a title bestowed upon persons who rule others. this is my definition.maybe, by some christians the word lord is used to refer to god, but being used in this way by christians does not make it the same thing. so, this verse does not say that spirit is god.and then he gave some similarities or same attributes of GOD&SON&SPIRIT, by this he argues that it is reference for the godness of the SPIRIT.{The Father is eternal (Ps 90:2), and the Son (Isa 9:6; Mic 5:2), and the Holy Spirit (Heb 9:14)The Father is omniscient (1 John 3:20), and the Son (John 16:30; 21:17), and the Holy Spirit (1 Cor 2:10-11)The Father is omnipresent (1 Kings 8:27; Ps 137:8-18), and the Son (Matt 18:20), and the Holy Spirit. (Ps 137:7)The Father is omnipotent (Dan 4:35), and the Son (Matt 28:18; John 17:10), and the Holy Spirit (Isa 40:12-18)} having the same attributes does not mean that that things are the same one thing.for example, people breathe and at the same time donkeys also breathe. does it mean that donkeys are people or people are donkeys?so, this similarities or same attributes does not mean that they are one thing.(5)in the fifth arguement of his, he again talked about the godness of Jesus. in fact, I consider this arguement is wrong but I dont need to refute this since I agreed with PRO that he showed us verses from bible that talk about the godness of SON[/jesus]SUMMARY: PRO has shown the godness of son and father but he has not shown the reference talk about the godness of spirit. all he did is to interprete some verses as if it says that spirit is god.additional:sometimes when I quoted my opponent, I shortened to have character sufficiency or to avoid character insufficiency.good luck. Report this Argument Pro daley forfeited this round. Con since we are allowed to forfeit, I guess my opponent will come with answers in next round.I am con this debate and in this round I have no burden from previous one, hence I am going to present some arguements of mine against Trinity, my opponent will reply to it.Christians are amazing, Bible does not contain any explicit mention of the doctrine of Trinity, though there are several fragments claimed to indirectly support it. EVEN THOUGH There are also several fragments that appear to explicitly deny it, STILL THIS IS NOT A PROBLEM FOR THEM. (1)passages contradict trinity "But about that day or hour no one knows, not even the angels in heaven, nor the Son, but only the Father." mark13:32 NIV if father and spirit and son was ONE, then let us consider that Jesus broke his divinity and at that time Jesus was not one with spirit&father, now we conclude that: Father and spirit was one. if that two were one, then the spirit could have known due to oneness, but the verse says: ONLY FATHER KNOWS IT. this contradicts the oneness of spirit&father. {I am not including Jesus since we accepted him not god at that time.}JOhn17:3 reads:"“Father, the hour has come. Glorify your Son, that your Son may glorify you. 2 For you granted him authority over all people that he might give eternal life to all those you have given him. 3 Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent" here, Jesus [himself] says that "father is the only true GOD." it contradicts the trinity due to according to trinity Spirit is also god, jesus says "ONLY"we may conclude that this words of Jesus is against the godness of the spirit [and also godness of him].(2)interpreting trinity with logic rationally[1]:(I hope this image will be available to see, if not available: http://rationalwiki.org...) The shield presents the following 12 statements simultaneously: "The Father is God" "The Son is God" "The Holy Spirit is God" "God is the Father" "God is the Son" "God is the Holy Spirit" "The Father is not the Son" "The Son is not the Father" "The Father is not the Holy Spirit" "The Holy Spirit is not the Father" "The Son is not the Holy Spirit" "The Holy Spirit is not the Son Since $\forall A,B \in X: \left(A \subseteq B \and B \subseteq A\right) \Rightarrow A = B$, the statements 1-6 can be restated as follows: God = FatherGod = SonGod = Holy Spirit while the statements 7-12 can be restated as:Father ≠ SonFather ≠ Holy SpiritSon ≠ Holy Spirit Conventional logic says that equality is transitive: $\forall A,B,C \in X: \left( A = B \and B = C \right) \Rightarrow A = C$. Let's start from one of the "is not" relations. Father ≠ Son Now let's substitute the left side with the statement "God = Father": God ≠ Son and then substitute the right side with "God = Son": God ≠ God Further application of transitivity leads to the following statements: Son ≠ SonFather ≠ FatherHoly Spirit ≠ Holy Spirit We conclude that God is not God, and so the doctrine of the Trinity implies that God as well as all three persons of the Trinity violate the law of identity. One of the fundamental assumptions of conventional logic is that objects that violate the law of identity do not exist: there is no entity that is not itself. This means several things: If Trinity is true, then God does not exist, and neither do any of his three persons. If God exists, then by the law of noncontradiction Trinity is a false doctrine. If God exists and Trinity is true, it can mean two things: Logic is meaningless, because it is possible to prove anything, including the existence and the non-existence of God. Trinity means something else than its Christian definition. in round one, my opponent brought things which he interpreted and used them as if they support trinity, after that I wanted to present this arguement against him, in first round with his arguement#2 he did it, as he did I also used this as an arguement. even if he brings up [which he didnt in two rounds] verses from the bible which completes the challenge of: verses/reference from the bible that: talks about the godness of the father. talks about the godness of the son. talks about the godness of the hole spirit. then this analys of rational wiki destroys it. (3) video I want to recommend to watch:*these are not arguement and has no relation with the topic, I just offered it, opponent does not need to refute this according to the debate purpose.I think these are enough. source: Report this Argument Pro daley forfeited this round. Con in fact, PRO needs to set arguements for the existence of trnity['s concept] in the bible but since he has been forfeiting for 2 rounds, I am going to set my arguements which are against trinity so that the purpose of the debate will be met, the debate is to clarify whether trinity is supported by bible or protested by bible. he has shown 2/3 of the challenge, remaining one is the godness of spirit in the bible.I dont know why my opponent forfeited, considering we are allowed to forfeit I think he will come with answers, but I dont want to waste this round, I am goiing to present 2-3 arguements from the bible which contradict the doctrine of trinity.1) according to the arguement of my opponent, Jesus is father, father is Jesus, they are one. holy spirit as well. [reference: his second arguement on the first round]definition of wikipedia does not say such, but if my opponent believes in that way, ok, no problem. I will argue considering Jesus as father and spirit as well.against this case, I am going to bring one arguement:NIV JOHN20:17"17 Jesus said, “Do not hold on to me, for I have not yet ascended to the Father. Go instead to my brothers and tell them, ‘I am ascending to my Father and your Father, to my God and your God.’”"now, if Jesus and father [holy spirit as well] is one, it means that: "where is Jesus, there is father, where is father there is Jesus", "what Jesus is doing is what father is doing, what father is doing is waht Jesus is doing" but, when we read John 20:17, is this verse is reasonable to deduce that it contradicts the arguement of PRO?if Jesus and father was one Jesus wouldnot have said: "for I have not yet ascended to the Father"because anywhere Jesus is present, he is with father according to the definition of PRO, Jesus is himself father but Jesus says "I have not yet ascended to father". reading this, we can conclude that Jesus and father are seperate.2)second arguement I am going to present is: "21 “Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. 22 Many will say to me on that day, ‘Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?’ 23 Then I will tell them plainly, ‘I never knew you. Away from me, you evildoers!’" now, if Jesus and father was one or Jesus was god, he would not have said it.a) If Jesus and father are one, then Jesus contradicts logic. he says: "Not everyone who says to me, ‘Lord, Lord,’ will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven." here, referring Jesus as god is equal to referring to father since he was himself father/god.b) in case Jesus is father himself, then here he is contradicting himself, since he was a father, it is irrational to say: "but only the one who does the will of my Father who is in heaven." the will of my father he says, if he is his own father, then he would not make diffrence between the will of Jesus vs the will of Father.these two is enoguh I think. I wanna add:3)one of the most widely used arguement for trinity if not the most one is:"For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one." 1john5:7with this verse christians try to support trinity.my opinion about it: in this verse it can not be seen anywhere that Jesus Christ is God or can be associated with God or being an equal to God. even more, when you read the verse before it, it is reasonable to deduce that that verse says Jesus is man, not god."This is he that came by water and blood, even Jesus Christ; not by water only, but by water and blood. And it is the Spirit that beareth witness, because the Spirit is truth."when you read it in context, more than trinity, this passage seems to be supporting the personhood of Jesus, not his godness.these are enough.if my opponent forfeits in this round too, I am not going to set arguements in the next one. I am just going to write something so that the time will not be wasted. Report this Argument Pro daley forfeited this round. Con if my opponent still forfeits and leaves no reply, then all I can do is to hope that the aim the debate had been met and you have enjoyed this. to not become tie, vote CONReport this Argument Pro daley forfeited this round.
9 comments have been posted on this debate. Showing 1 through 9 records.
Posted by Artur 3 years ago
@abraralam, can you give me a reference for the things you said? from authoritive, objective scientif source? not a site of islamic group or team.
Posted by Artur 3 years ago
@abraralam, are you advertising your religion? I know about your religion too, I have read about it, I have read the quran, I dont think that islam is the true one, if you want we can debate it. I will challenge you after this debate, do you want it?

Btw, I see islam as the most logical/rational religion but not the truth.
Posted by abraralam 3 years ago
Natural, Neutral and Irrefutable Proofs on Truth of Islam
The Earth: (1)
The Earth is a nature. It cannot tell a lie. It cannot favor or support wrong thinking or wrong beliefs or wrong lifestyles. It is 100% true and neutral. This obeys only true God or true followers of God. It doesn't obey any other fabricated Gods or any followers of fabricated Gods or any Atheists.
The irrefutable proof on above commentary is that there are hundreds of fresh dead bodies with fresh blood of Muslim Martyrs and saints who are preserved from decay in their graves since centuries and years without used any chemicals. Once we had dug their graves for any reasons, we found them in above condition, our doctors examined them and there are thousands of eyewitnesses too. We will not dig their graves again for every person on his desire now because you non-Muslims are 5 billion at this time in the world.
So, if you are sincere for truth, but you do not trust us, then contact us with your doctors, researchers and media team about the research of these fresh dead bodies. If you refuted above research, we will pay you 1 million dollars and we will be ready for any punishment from you in front of world media otherwise accept our research and enter in Islam. Do not see condition of some bad Muslims because the Islam is perfect, but all Muslims are not perfect.
According to my research there is no fresh dead body with fresh blood of any Atheists and Non-Muslims that is preserved from decay under the Earth or on the Earth since centuries and years without used any chemicals. So it is 100% proof that there are no other Gods except Almighty Allah and the nature Earth doesn't support or obey any fabricated Gods (except Almighty Allah) or followers of fabricated Gods or Atheists.
Posted by abraralam 3 years ago
The Air: (2)
The Air is a nature. It cannot tell a lie. It cannot favor or support wrong thinking or wrong beliefs or wrong lifestyles. It is 100% true and neutral. It obeys only true God or true followers of God. It doesn't obey any other fabricated Gods or any followers of fabricated Gods or any Atheists.
The 100% proof on it is that if you leave intact dead bodies of all soldiers on the Earth who fought against each other in the name of their Gods and religion, then after death only Muslim Martyrs will remain in fresh condition with fresh blood and their enemies will decay.
There are two questions to all Atheists and Non-Muslims:
1) The Muslim soldiers who are slain in the way of Islam, why their dead bodies remain in fresh condition with fresh blood? And, all Atheists and all Non-Muslims soldiers who are murdered in the way of their religions, why their dead bodies do not remain in fresh condition with fresh blood?
2) Why the God did not preserve your soldiers' dead bodies who sacrificed for Him and why the God of Islam Almighty Allah preserved the dead bodies with fresh blood of those Muslim soldiers who sacrificed for Him?
Posted by abraralam 3 years ago
The Fire: (3)
It is perfect that the Fire is a nature. It does not have any capacity to save any human body in it. So, if a Muslim goes in it without using any chemicals and he is immune to burn, then it will be a miracle and a 100% proof on truth of Islam. And, look how intransigents are majority of Atheists and Non-Muslims that they do not agree to demonstrate such miracle and if we Muslims are ready to demonstrate such miracle (by the mercy of Allah) then they are not even willing to convert to Islam.
Dear Atheists and non-Muslims, I ask you that if a Muslim goes in Fire without using any chemical on his body in front of world media and he is immune to burn in it, then will you all convert to Islam or not?
If yes, then fix a time, date and place and start announcement in whole world because you are 5 billion and it is impossible that we enter in Fire for every Atheists and Non-Muslims for proving the truth of Islam.
Posted by abraralam 3 years ago
The Water: (4)
The water is a nature. Our claim is that it only obeys the God of Islam or only true followers of God of Islam. So please study following research and event that is proof on our claim
Prophet Moses and his followers (peace be upon them) were escaping from Egypt. When they reached to the Red Sea, they prayed to Almighty Allah. Allah the exalted said to Prophet Moses (peace be upon him) to hit the Red Sea with his staff. When the Prophet Moses (peace be upon him) hit the Red Sea, then sea split in two parts and they found the open path to cross the sea. So, the Prophet Moses and his followers (peace be upon them) crossed the sea.
The Pharaoh Ramesses and his army who were chasing the Prophet Moses and his followers (peace be upon them) reached to Red Sea. They found the open path, so they walked on dry ground following them, but when they reached in the middle of Red Sea, the sea joined back on them and they drown in it.
After this event, Almighty Allah saved the dead body of Pharaoh forever as a sign for Atheists and Non-Muslims.
So according to head of archaeologist and anatomical scientists the Professor Maurice Bucaille (who converted to Islam after his research) and according to Holy Quran, Pharaoh Ramesses died in the Red Sea following the Prophet Moses and his followers (peace be upon them).
For details on research of Professor Maurice Bucaille on this event please study "The Dead body of Pharaoh" in the article section on www.rightfulreligion.com.
Commentary on this event:
(1) This event is 100% true. So this event proves that there is existence of a God Almighty Allah (who is God of Islam and the God of Prophet Moses) because the Prophet Moses (peace be upon him) hit the red sea via his staff by the order of Almighty Allah and the red sea obeyed the Prophet Moses (peace be upon him) and his God Almighty Allah.
(2) This event also proves that water obeys the God Almighty Allah and His true followers because when the Prophet Moses (peac
Posted by abraralam 3 years ago
" Gospel of John chapter no 14, verse no 28.... Jesus said: My father is greater than I." Because this verse says clearly that Jesus is great and his father is greater. It is perfect according to commonsense that great person and a greater person can not be equal in power and they are different persons not one. Please tell me if you say that your brother is older than you, then any one who have sense can say that you and your brother are one.?

So, either your Bible is a mixed book and has contradiction in it or either your belief is wrong. And then where is your belief of trinity? Can you refute this verse from Bible? Remeber, if your beliefs will not be true you will not be saved from Hell hereafter.

Holy Quran Surah no 4 verse no 171,
"0 people of the Book, be not excessive in your Faith and do not say about Allah anything but the truth. The Masih 'fsa, the son of Maryam, is only a Messenger of
Allah and His word He delivered to Maryam, and a spirit from Him. So, believe in Allah and His Messengers. And do not say 'Three". Stop it. That is good for you. Allah is the only One God. He is far too pure to have a son. To Him belongs what is in the heavens and what is in the earth. And Allah is enough to trust in."

So, Jesus (peace be upon him) is only a great Messenger of Allah, His word, His spirit but he isn"t a God or son of God or third of the three. So you can love him , serve him and remember him, but you can not worship him. You should worship his God Almighty Allah because he worshipped Him.
Posted by Artur 3 years ago
5 is good.
Posted by xXCryptoXx 3 years ago
Lower this to three rounds and I'll take it.
1 votes has been placed for this debate.


text:
# Bluff (poker)

In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the term is often used outside the context of poker to describe the act of making threats one cannot execute.

## Pure bluff

A pure bluff, or stone-cold bluff, is a bet or raise with an inferior hand that has little or no chance of improving. A player making a pure bluff believes he can win the pot only if all opponents fold. The pot odds for a bluff are the ratio of the size of the bluff to the pot. A pure bluff has a positive expectation (will be profitable in the long run) when the probability of being called by an opponent is lower than the pot odds for the bluff.

For example, suppose that after all the cards are out, a player holding a busted drawing hand decides that the only way to win the pot is to make a pure bluff. If the player bets the size of the pot on a pure bluff, the bluff will have a positive expectation if the probability of being called is less than 50%. Note, however, that the opponent may also consider the pot odds when deciding whether to call. In this example, the opponent will be facing 2-to-1 pot odds for the call. The opponent will have a positive expectation for calling the bluff if the opponent believes the probability the player is bluffing is at least 33%.

## Semi-bluff

In games with multiple betting rounds, to bluff on one round with an inferior or drawing hand that might improve in a later round is called a semi-bluff. A player making a semi-bluff can win the pot two different ways: by all opponents folding immediately or by catching a card to improve the player's hand. In some cases a player may be on a draw but with odds strong enough that he is favored to win the hand. In this case his bet is not classified as a semi-bluff even though his bet may force opponents to fold hands with better current strength.

For example, a player in a stud poker game with four spade-suited cards showing (but none among their downcards) on the penultimate round might raise, hoping that his opponents believe he already has a flush. If his bluff fails and he is called, he still might be dealt a spade on the final card and win the showdown (or he might be dealt another non-spade and try his bluff again, in which case it is a pure bluff on the final round rather than a semi-bluff).

## Bluffing circumstances

Bluffing may be more effective in some circumstances than others. Bluffs have a higher expectation when the probability of being called decreases. Several game circumstances may decrease the probability of being called (and increase the profitability of the bluff):

• Fewer opponents who must fold to the bluff.
• The bluff provides less favorable pot odds to opponents for a call.
• A scare card comes that increases the number of superior hands that the player may be perceived to have.
• The player's betting pattern in the hand has been consistent with the superior hand they are representing with the bluff.
• The opponent's betting pattern suggests the opponent may have a marginal hand that is vulnerable to a greater number of potential superior hands.
• The opponent's betting pattern suggests the opponent may have a drawing hand and the bluff provides unfavorable pot odds to the opponent for chasing the draw.
• Opponents are not irrationally committed to the pot (see sunk cost fallacy).
• Opponents are sufficiently skilled and paying sufficient attention.

The opponent's current state of mind should be taken into consideration when bluffing. Under certain circumstances external pressures or events can significantly impact an opponent's decision making skills.

## Optimal bluffing frequency

If a player bluffs too infrequently, observant opponents will recognize that the player is betting for value and will call with very strong hands or with drawing hands only when they are receiving favorable pot odds. If a player bluffs too frequently, observant opponents snap off his bluffs by calling or re-raising. Occasional bluffing disguises not just the hands a player is bluffing with, but also his legitimate hands that opponents may think he may be bluffing with. David Sklansky, in his book The Theory of Poker, states "Mathematically, the optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting."

Optimal bluffing also requires that the bluffs must be performed in such a manner that opponents cannot tell when a player is bluffing or not. To prevent bluffs from occurring in a predictable pattern, game theory suggests the use of a randomizing agent to determine whether to bluff. For example, a player might use the colors of his hidden cards, the second hand on his watch, or some other unpredictable mechanism to determine whether to bluff.

Example (Texas Hold'em)

Again, let us return to the examples in The Theory of Poker:

when I bet my $100, creating a$300 pot, my opponent was getting 3-to-1 odds from the pot. Therefore my optimum strategy was . . . [to make] the odds against my bluffing 3-to-1.

Since the dealer will always bet with (nut hands) in this situation, he should bluff with (his) "Weakest hands/bluffing range" 1/3 of the time in order to make the odds 3-to-1 against a bluff.[1]

Ex: On the last betting round (river), Worm has been betting a "semi-bluff" drawing hand with: A♠ K♠ on the board:

10♠ 9♣ 2♠ 4♣ against Mike's A♣ 10♦ hand.

The river comes out:

2♣

The pot is currently 30 dollars, and Worm is contemplating a 30 dollar bluff on the river. If Worm does bluff in this situation, he is giving Mike 2-to-1 pot odds to call with his two pair (10's and 2's).

Important: In these hypothetical circumstances, Worm will have the nuts 50% of the time, and be on a busted draw 50% of the time. Worm will bet the nuts (100%) of the time, and bet with a bluffing hand (using mixed optimal strategies):

$x = s/(1+s)$ [2]

Where s is equal to the percentage of the pot that Worm is bluff betting with and x is equal to the percentage of busted draws Worm should be bluffing with to bluff optimally.

Pot = 30 dollars. Bluff bet = 30 dollars.

s = 30(pot) / 30(bluff bet) = 1.

Worm should be bluffing with his busted draws:

x = $1/(1+s) = 50%$ Where s = 1

Assuming 4 trials, Worm has the nuts 2 times, and has a busted draw 2 times. (EV = Expected Value)

Worm bets with the nuts (100% of the time) Worm bets with the nuts (100% of the time) Worm bets with a busted draw (50% of the time) Worm checks with a busted draw (50% of the time)
Worm's EV = 60 dollars Worm's EV = 60 dollars Worm's EV = 30 dollars (if Mike folds) and -30 dollars (if Mike calls) Worm's EV = 0 dollars (since he will neither win the pot, nor lose 30 dollars on a bluff)
Mike's EV = -30 dollars (because he would not have won the original pot, but lost to Worm's value bet on the end) Mike's EV = -30 dollars (because he would not have won the original pot, but lost to Worm's value bet on the end) Mike's EV = 60 dollars (if he calls, he'll win the whole pot, which includes Worm's 30 dollar bluff) and 0 dollars (if Mike folds, he can't win the money in the pot) Mike's EV = 30 dollars (assuming Mike checks behind with the winning hand, he will win the 30 dollar pot)

Under the circumstances of this example: Worm will bet his nut hand 2 times, for every one time he bluffs against Mike's hand (assuming Mike's hand would lose to the nuts and beat a bluff). This means that (if he called all three bets) Mike would win 1 time, and lose two times, and would break even against 2-to-1 pot odds. This also means that Worm's odds against bluffing is also 2-to-1 (since he will value bet twice, and bluff once).

Say in this example, Worm decides to use the second hand of his watch to determine when to bluff (50% of the time). If the second hand of the watch is between 1 and 30 seconds, Worm will check his hand down (not bluff). If the second hand of the watch is between 31 and 60 seconds, Worm will bluff his hand. Worm looks down at his watch, and the second hand is at 45 seconds, so Worm decides to bluff. Mike folds his two pair saying, "the way you've been betting your hand, I don't think my two pair on the board will hold up against your hand." Worm takes the pot by using optimal bluffing frequencies.

Please note: This example is meant to illustrate how optimal bluffing frequencies work. Because it was an example, we assumed that Worm had the nuts 50% of the time, and a busted draw 50% of the time. In real game situations, this is not usually the case.

The purpose of optimal bluffing frequencies is to make the opponent (mathematically) indifferent between calling and folding. Optimal bluffing frequencies are based upon game theory and the Nash Equilibrium, and assist the player using these strategies to become unexploitable. By bluffing in optimal frequencies, you will typically end up breaking even on your bluffs (in other words, optimal bluffing frequencies are not meant to generate positive expected value from the bluffs alone). Rather, optimal bluffing frequencies allow you to gain more value from your "value bets," because your opponent is indifferent between calling or folding when you bet (regardless to whether it's a value bet or a bluff bet).[3]

## Bluffing in other games

Although bluffing is most often considered a poker term, similar tactics are useful in other games as well. In these situations, a player makes a play that shouldn't be profitable unless an opponent misjudges it as being made from a position capable of justifying it. Since a successful bluff requires deceiving one's opponent, it occurs only in games where the players conceal information from each other. In games like chess and backgammon where both players can see the same board, they should simply make the best legal move available. Examples include:

• Contract Bridge: Psychic bids and falsecards are attempts to mislead the opponents about the distribution of the cards. A risk (common to all bluffing in partnership games) is that a bluff may also confuse the bluffer's partner. Psychic bids serve to make it harder for the opponents to find a good contract or to accurately place the key missing cards with a defender. Falsecarding (a tactic available in most trick taking card games) is playing a card that would naturally be played from a different hand distribution in hopes that an opponent will wrongly assume that the falsecarder made a natural play from a different hand and misplay a later trick on that assumption.
• Stratego: Much of the strategy in Stratego revolves around identifying the ranks of the opposing pieces. Therefore depriving your opponent of this information is valuable. In particular, the "Shoreline Bluff" involves placing the flag in an unnecessarily vulnerable location in hopes that the opponent won't look for it there.
• Spades: In late game situations, it is useful to bid a nil even if it cannot succeed.[4] If the third seat bidder sees that making a natural bid would allow the fourth seat bidder to make an uncontestable bid for game, he may bid nil even when it has no chance of success. The last bidder then must choose whether to make his natural bid (and lose the game if the nil succeeds) or to respect the nil by making a riskier bid that allows his side to win even if the doomed nil is successful. If he chooses wrong and both teams miss their bids, the game continues.
• Scrabble: Scrabble players will sometimes deliberately play a phony hoping the opponent doesn't challenge it. Bluffing in Scrabble is a bit different from the other examples. Although Scrabble players do conceal their tiles, they have little opportunity to make significant deductions about their opponent's tiles, and even less opportunity to spread disinformation about them. Bluffing by playing a phony is instead based on assuming players have imperfect knowledge of the acceptable word list.


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# Math Help - Non-right angled trig.

1. ## Non-right angled trig.

I tried to solve this question and got the answer to be 79.8 m.
The correct answer is apparrantly 204 m.
I hope you can help me solve this question.

The question:
From point A, the angle of elevation to the top a tall building is 20 degrees. On walking 80 m towards the building the angle of elevation is now 23 degrees. How tall is the building?

Thanks,
Amine

2. You effectively have a right angled triangle split into a smaller right angled triangle, and an irregular triangle. first you can work out the angles inside the iregular triangle.

$180=20+(180-23)+A \implies A=3^{\circ}$

Next you can use the sine rule to find the hypotenuse of the smaller right angled triangle:

$\frac{80}{\sin(3)}=\frac{c}{\sin(20)}\implies c = 522.81m
$

then the height of the building h is given by:

$h=522.81\sin(23)=204.3m$

I tried to solve this question and got the answer to be 79.8 m.
The correct answer is apparrantly 204 m.
I hope you can help me solve this question.

The question:
From point A, the angle of elevation to the top a tall building is 20 degrees. On walking 80 m towards the building the angle of elevation is now 23 degrees. How tall is the building?

Thanks,
Amine
Have a look here: http://www.mathhelpforum.com/math-he...879-post2.html

second question.


text:
This vignette describes the importance of indirect relations on networks, how they are used in centrality indices and how they are implemented in the netrankr package.

## Theoretical Background

A one-mode network can be described as a dyadic variable $$x\in \mathcal{W}^\mathcal{D}$$, where $$\mathcal{W}$$ is the value range of the network (in the simple case of unweighted networks $$\mathcal{W}=\{0,1\}$$) and $$\mathcal{D}=\mathcal{N}\times\mathcal{N}$$ describes the dyadic domain of actors $$\mathcal{N}$$.

Observed presence or absence of ties (the value range is binary) is usually not the relation of interest for network analytic tasks. Instead, mostly implicitly, relations are transformed into a new set of indirect relations on the basis of the observed relations. As an example, consider (geodesic) distances in the underlying graph. While they are fairly easy to derive from an observed network of contacts, it is impossible for actors in a network to answer the question “How far away are you from others you are not connected with?”. We denote generic transformed networks from an observed network $$x$$ as $$\tau(x)$$.

With this notion of indirect relations, we can express all centrality indices in a common framework as $c_\tau(i)=\sum\limits_{t \in \mathcal{N}} \tau(x)_{it}$ Degree and closeness centrality, for instance, can be obtained by setting $$\tau=id$$ and $$\tau=dist$$, respectively. Others need several additional specifications which can be found in Brandes (2016) or Schoch & Brandes (2016).
With this framework, all centrality indices can be characterized as degree-like measures in a suitably transformed network $$\tau(x)$$.

## Indirect relations in the netrankr package

library(netrankr)
library(igraph)

The netrankr package implements a great variety of indirect relations that are (or could be) used for centrality related considerations in a network. All indirect relations can be computed with the indirect_relations() function, by specifying the type parameter.

g <- graph.empty(n=11,directed = FALSE)
6,10,6,11,7,9,7,10,7,11,8,9,8,10,9,10))
V(g)\$name <- 1:11

A <- indirect_relations(g,type="identity")
#geodesic distances
D <- indirect_relations(g,type="geodesic")
#dyadic dependencies (as used in betweenness centrality)
B <- indirect_relations(g,type="dependencies")
#resistance distance (as used in information centrality)
R <- indirect_relations(g,type="resistance")

The function takes an additional parameter FUN which passes an additional function to further specify the transformation. The main use is to obtain walk based indirect relations

#count the limit proportion of walks (used for eigenvector centrality)
W <-  indirect_relations(g,type="walks",FUN=walks_limit_prop)
#count the number of walks of arbitrary length between nodes, weighted by
#the inverse factorial of their length (used for subgraph centrality)
S <-  indirect_relations(g,type="walks",FUN=walks_exp)

Additional parameters can also be passed to calculate parameterized versions of relations.

#Calculate dist(s,t)^-alpha
D <- indirect_relations(g,type="geodesic",FUN=dist_dpow,alpha=2)

To view all predefined transformation functions type ?transform_relations. The predefined functions follow the naming scheme <relation>_<transformation>. The functions dist_ are thus only meaningful for type="geodesic" or type="resistance" and walks_ for type="walks". The predefined functions are not exhaustive and just constitute the most common transformations. It is, however, straightforward to pass your own transformation function.

dist_integration <- function(x){
x <- 1 - (x - 1)/max(x)
}
D <- indirect_relations(g,type="geodesic",FUN=dist_integration)

The function dist_integration() computes $\tau(x)_{ij}=1-\frac{dist(i,j)-1}{max_{i,j}\; dist(i,j)}$ which is used in the centrality index integration defined by Valente and Foreman (1998)


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# Homework Help: Circular motion in a magnetic field

1. Aug 3, 2015

### kaspis245

1. The problem statement, all variables and given/known data
Small mass $m$ ball has a negative charge $q$ and is hanging on an inelastic string which has a length of $l$. What is the smallest velocity that one need to impart on this ball for it to make one revolution? There is also a uniform magnetic field $B$ as shown in the drawing.

2. Relevant equations
$F=Bqv$
$F_c=\frac{mv^2}{r}$

3. The attempt at a solution
We need to find $v_o$

Conservation of energy:
(1) $\frac{mv_o^2}{2}=2mgl+\frac{mv^2}{2}$

The force $F=Bqv$ always points into the center of the circle. When the ball reaches the top of the circle, it will be affected by two forces $F=Bqv$ and $mg$. Both point downwards, hence the sum of those forces must be the centripetal force.
(2) $Bqv+mg=\frac{mv^2}{l}$

Now I can express v from this equation and place it into (1). Is that correct?

2. Aug 3, 2015

### SammyS

Staff Emeritus
Yes. That looks to be correct.

3. Aug 3, 2015

### kaspis245

Please check if my final answer is correct.

$mv^2-Bqlv-mgl=0$
$v=\frac{Bql+\sqrt{B^2q^2l^2+4m^2gl}}{2m}$

$v_o=\sqrt{4lg+\frac{Bql+\sqrt{B^2q^2l^2+4m^2gl}}{2m}}$

4. Aug 3, 2015

### TSny

I think this expression for $v$ is correct.

Did you forget to square $v$ when you substituted for $v$ inside the radical?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

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text:
# Plot with Color Data as Third Coordinate of Ordered Pairs

Suppose I have a data set

data={{0,0,-1},{0,1,-0.5},{1,1,0},{2,1,0.5},{2,2,1}};

where the first two coordinates are x and y values, and the third is input for the color gradient function

crgrad[x_] := Blend[{{-1, Blue},{0, Black}, {1, Red}}, x];

What is the correct way to plot the data points and have each point be its corresponding color? I have already tried

dataPlt = Graphics[{Point[{#1, #2}], ColorFunction -> (crgrad[#3])} & @@@ data];

I also want to incorporate

ColorFunctionScaling -> False

Thanks!

• Graphics[{crgrad[#3], Point[{#1, #2}]} & @@@ data]? – kglr Mar 29 '16 at 5:10
• Thanks for the reply, but that also does not work. – S2167 Mar 29 '16 at 6:04

If you do not have to use ColorFunction, you can use

Graphics[{crgrad[#3], PointSize[.05], Point[{#1, #2}]} & @@@ data]

or

Graphics[{PointSize[.05], Point[{#1, #2}, VertexColors -> crgrad[#3]]} & @@@ data]

or

ListPlot[Style[{#, #2}, crgrad[#3], PointSize[.05]] & @@@ data,
Axes -> False, PlotRangePadding -> .2, AspectRatio -> 1]

• For some reason I could not get the method to work after reading your comment, but it now works brilliantly. Thank you. – S2167 Mar 29 '16 at 7:07
• @S2167, thank you for the accept. – kglr Mar 29 '16 at 8:31


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# Recent questions tagged generating-functions

1
Let $C_i(i=0,1,2...n)$ be the coefficient of $x^i$ in $(1+x)^n$.Then $\frac{C_0}{2} – \frac{C_1}{3}+\frac{C_2}{4}-\dots +(-1)^n \frac{C_n}{n+2}$ is equal to $\frac{1}{n+1}\\$ $\frac{1}{n+2}\\$ $\frac{1}{n(n+1)}\\$ $\frac{1}{(n+1)(n+2)}$
2
The generating function of the sequence $\left \{ a_{0},a_{1},a_{2}..........a_{n}………...\infty \right \}$ where $a_{n}=\left ( n+2 \right )\left ( n+1 \right ).3^{n}$ is $a)3\left ( 1+3x \right )^{-2}$ $b)3\left ( 1-3x \right )^{-2}$ $c)2\left ( 1+3x \right )^{-3}$ $d)2\left ( 1-3x \right )^{-3}$
3
Find the generating function for the sequence $\left \{ a_n \right \} where$ $a_n = \Large \binom{10}{n+1}$ for n = 0,1,2, . Sol. $\Large \binom{10}{1} + \binom{10}{2}x + \binom{10}{3}x^2 + \binom{10}{4} x^3 + .... + \binom{10}{10}x^{9}$ multiplying and dividing above equation ... , $\Large - \frac{1}{x} + \frac{1}{x} ( 1+x)^{10}$ $\Large \color{red}{ \frac{( 1+x )^{10} - 1}{x} }$ Please verify
4
1 vote
5
Let We define Then ar is equal to. $\binom{r}{2019}$ $\binom{r}{r + 2018}$ $\binom{r}{2019 – r}$ $\binom{r}{r – 2018}$ Can anyone tell me if this type of question is in Gate 2019 syllabus or not because I have never seen such question in previous year question? If yes, then when can I learn this stuff from. Because I am unable to understand the whole solution.
1 vote
6
For each of these generating functions, provide a closed formula for the sequence it determines. $a) (3x − 4)^{3}$ $b) (x^{3} + 1)^{3}$
7
Which one of the following best expresses the generating function sequence $\{a_n\}$, for the given closed form representation? $F(x) = \frac{1}{1-x-x^2}$ $a_n=a_{n-1}+3, n>0, a_0=1$ $a_n=a_{n-1}+a_{n-2}, n>1, a_0=1, a_1=1$ $a_n=2n+3, n>1$ $a_n=2a_{n-1}+3, n>1, a_0=1$
8
Let $M(x) = \frac{x^{2018}}{(1-x)^{2019}}$ we define $M(x) = \sum_{r=0}^{\infty}a_{r}x^{r}$ ,then $a_{r}$ is equal to- $A)\binom{r}{2019}$ $B)\binom{r}{r+2018}$ $C)\binom{r}{2019-r}$ $D)\binom{r}{r-2018}$
1 vote
9
The number of ways can 10 balls be chosen from an urn containing 10 identical green balls, 5 identical yellow balls and 3 identical blue balls are __________ .
10
Difference between getting closed form of generating function and closed form of the given sequence ,pls someone explain with an example
11
Find a closed form for the exponential generating function for the sequence $\{a_n\}$ where $a_n=\frac{1}{(n+1)(n+2)}$ I broke it down into partial fractions and got $a_n=\frac{1}{n+1}-\frac{1}{n+2}$ ... $\sum_{n=0}^{\infty}\frac{1}{(n+2)}.\frac{x^n}{n!}$
12
Use Generating function to determine,the number of different ways $10$ identical balloons can be given to four children if each child receives atleast $2$ ballons? Ans given $(x^{2}+x^{3}+.........................)^{4}$ But as there is a upper bound I think answer will be $(x^{2}+x^{3}+.........................+{\color{Red} {x^{10}}})^{4}$ Which one is correct? plz confirm
1 vote
13
How to find coefficient of $x^{100}$? $= (1+x^{10}+(x^{10})^2 + \dots)(1+x^{20}+(x^{20})^2 + \dots)(1+x^{50}+(x^{50})^2 + \dots)\\ = (\frac{1}{1-x^{10}}).(\frac{1}{1-x^{20}}).(\frac{1}{1-x^{50}})$
1 vote
14
What will be solution of this function for coefficient of $x^{100}$? $\frac{1}{\left ( 1-x^{10} \right )(1-x^{20})(1-x^{50})}$
15


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# What is Production Possibility Frontier (PPF) diagram drawn on consumption-leisure?

When explaining basic macroeconomics model involving consumption-leisure tradeoff, often diagram showing production possbility frontier (PPF) is drawn with leisure on x-axis and consumption on y-axis. But what exactly is the meaning of this production possibility frontier?

Production Possibility Froniter diagram is often drawn on two-goods basis (for example, like butter on x-axis and milk on y-axis) but I am confused on what PPF might be on consumption-leisure basis.

Edited because wrnog answer, did not took the time to read the page.

Without maths

So your PPF would just be the link between leisure and consumption set by technology : the amount of leisure you choose give the time you can spend working, so the wage you earn and therefore the consumption you have (since there is no saving, all you earn is what you consume).

With a bit of math

You have a fixed amount of time, which we normalize to $1$. You can spend it either in leisure F (fun) or in work L (labour) so that $$1=L+F$$ Then you get a wage $w$, that is related to $L$ in some way : $w=\psi(L)$, and you consume $C=w=\psi(L)$, so that $L=\psi^{-1}(C)$

Then your PPF is $$F+\psi^{-1}(C)=1$$ It is a relation between leisure $F$ and consumption $C$ set by technology (the way wages are fixed).

Then the program is to maximize the agent utility $U(C,F)$ subject to this contraint. You can visualize it by the common tangent between iso-utility curves and your PPD.

• But in the reference link, iso-utility curve seems to be represented by curve I... – Newark Jan 16 '15 at 12:01
• I changed my answer, which was incorrect – Anthony Martin Jan 16 '15 at 13:37


text:
# Homework Help: Differential Equation (Homogeneous / scale-invariant

1. Mar 17, 2010

### PhysicsMark

1. The problem statement, all variables and given/known data
Test the following equation to show that they are scale invariant. Find their general solutions (It is not necessary to do the anti-derivative.)

$$(x+y^2)dy+ydx=0$$

I believe what my tutorial wants me to do is to check for homogeneity. I'm not sure though. This is not a Differential equations class, it is a math methods in physics class. The tutorial we use titles this section "Scale-invariant first-order differential equations".

3. The attempt at a solution

First I make the following substitutions:

$$x=\alpha{x}$$

$$y=\alpha^{n}x$$

I then use the substitutions in the DiffEq and solve for n so that the weight of each term is equal. I find that:

$$n=\frac{1}{2}$$

Based off that, I now make the following substitution:

$$y=v\sqrt{x}$$

From there things begin to get messy. I am unsure about 1 step so far: I am not sure what dy equates to. In the case that n=1, dy = vdx+xdv. I am not sure how to get dy using n=1/2.

Is it:

$$dy= vdx+{\sqrt{x}}dv$$

or:

$$dy= \frac{v}{2\sqrt{x}}+{\sqrt{x}dv$$

Or something else completely?

I guess I am asking what is dx in the equations above? Is it the derivative of x^1/2 or is it just dx?

2. Mar 17, 2010

### PhysicsMark

So it was something else completely. It is:

$$dy = \frac{v}{2\sqrt{x}}dx+{\sqrt{x}dv$$

I think I misunderstood basic differentiation notation.


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# Go-LaTeX

Date: 2019-10-03
Last Updated: 2019-10-03
GitHub: go-latex

I had an idea to use some Unicode characters in my Go projects, particularly ones that are physics or calculation based projects. But I personally did not want to have to either copy and paste the unicode characters or have to manually type in the unicodes for the various characters.

So I devised a solution, which was to write a simple parser that would regex out LaTeX commands for Greek letters and insert the correct character from a map stored within the application binary.

As of October 2019, I have released a β version to see what else can be implemented or how the idea can be improved upon.


text:
# Expected Failure Times Plot Example

This example appears in the Life Data Analysis Reference book.

In this example you will use the Expected Failure Times plot to estimate the duration of a planned reliability test. 4 units were allocated for the test, and the test engineers want to know how long the test will last if all the units are tested to failure. Based on previous experiments, they assume the underlying failure distribution is a Weibull distribution with $\beta = 2\,\!$ and $\eta = 500\,\!$.

Solution

Using Weibull++'s Expected Failure Times plot, the expected failure times with 80% 2-sided confidence bounds are given below.

From the above results, we can see the upper bound of the last failure is about 955 hours. Therefore, the test probably will last for around 955 hours.

As we know, with 4 samples, the median rank for the second failure is 0.385728. Using this value and the assumed Weibull distribution, the median value of the failure time of the second failure is calculated as:

\begin{align} & Q=1-{{e}^-{{{\left( \frac{t}{\eta } \right)}^{\beta }}}}\Rightarrow \\ & \ln (1-Q)={{\left( \frac{t}{\eta } \right)}^{\beta }} \\ & \Rightarrow t=\text{349.04}\\ \end{align}\,\!

Its bounds and other failure times can be calculated in a similar way.


text:
A long slope is formed in a soil with shear strength parameters$: c’=0$ and $\phi=34^{\circ}$. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use $\gamma_{sat} = 18 \: kN/m^3$ and $\gamma_u =10 \: kN/m^3$. The maximum slope angle (in degrees) to ensure a factor of safety of $1.5$, assuming a potential failure surface parallel to the slope, would be
1. $45.3$
2. $44.7$
3. $12.3$
4. $11.3$


text:
Previous | Next --- Slide 54 of 68
Back to Lecture Thumbnails
dvanmali

I noticed that Bernstein Basis seems a lot like applying a Taylor Series expansion with an increase in basis. Were these derived from a similar notion? Is so, couldn't we use a Taylor Series this?

theyComeAndGo

Why did we choose Bernstein basis instead of Taylor series, Fourier series etc.?

keenan

For one thing, because Bernstein bases are fairly localized in space and hence have a natural relationship with the control points. For instance, the coefficients of the first and last bases will directly determine the endpoints of the curve. For the cubic basis in particular, the other two coefficients give direct control over tangents at endpoints. In short: because this basis is natural for manipulating curves.

keenan

@dvanmali Also, if you take the 3rd-order Taylor series of a given function, you can always express it in the Bernstein basis. This basis is, after all, a basis for all cubic polynomials, not a special class of them. I would think of the Taylor series as more of a "procedure" for approximating a given function in terms of its kth derivatives; this (truncated) series can then be written down in any basis. The typical way to write it, of course, is just in the monomial basis 1, x, x^2, x^3, ..., but this basis isn't very good from the perspective of locality.


text:
• # question_answer Which of the following statements is not correct? A)  Terylene is a polyester polymer.B)  The monomer of natural rubber is butadiene.C)  Caprolactum is the monomer of nylon 6.D)  Phenol formaldehyde resin is known as 'Bakelite?

Monomer of natural rubber is isoprene. $\underset{(2-methylbuta-1,3-dience)}{\mathop{\underset{\text{Isoprene}}{\mathop{{{H}_{2}}C=\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,-CH=C{{H}_{2}}}}\,}}\,$ Hence, the correct option is [b].


text:
# How can i create a 3d curve/saddle shape?

I have tried and failed to use the Bezier Curve tool to create a 3D saddle shape only managing to bend a plane in one direction.

Is this the best way to do so and how should I go about doing it?

This is the shape i'm trying to create:

Thanks

• can you add a picture of what you want to create? Are you struggling with trying to get the plane to bend "around the horse" and arch front to back? – David Feb 15 '17 at 23:04
• I guess a subdivided plane driven by a lattice modifier would do the job perfectly, I'll make you a more detailed answer later. – Ahmed Ali Feb 16 '17 at 21:35

Bezier curves are not the proper tool for this, curves are useful mainly for extrusion based geometries, or sections-swept-along-paths shapes.

NURBS surfaces may be closer to what you need, though they will require some considerable manual modeling work, and they are a half-baked tool in Blender that wont help much.

You may also model this manually using meshes and subdivisions, but again will require a lot of manual modelling and not necessarily yield a mathematically accurate surface.

The best way to model such thing is using the builtin addon Add Mesh: Extra Objects Python script

Start by opening File > User Preferences > Addons then search for Extra and activate the Add Mesh: Extra Objects addon.

Then in the 3D View press Shift+A > Add > Mesh > Math Function > Z Math Function

According to Wikipedia the mathematical function for a simple Saddle Point surface is Z = X^2 - Y^2 so in the operator properties change the input formula to the desired function using Python notation which should be (x**2 - Y**2)

If you're just going for that look, and don't need mathematical precision,
Subdivide a plane then add a Simple Deform modifier using a sphere.

Do this twice. Once along the X-axis, and once along the Y-axis.

Set the Deform Angle positive for one of 'em,
and negative for the other.

You can see the technique illustrated here:


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# How do you solve 7^x=5^(x-4)?

Aug 22, 2015

Take $\log$ of both sides and use properties of $\log$ of exponents to find:

$x = \frac{- 4 \log \left(5\right)}{\log \left(7\right) - \log \left(5\right)} \approx - 19.133$

#### Explanation:

Take $\log$ of both sides to get:

$x \log \left(7\right) = \log \left({7}^{x}\right) = \log \left({5}^{x - 4}\right) = \left(x - 4\right) \log \left(5\right)$

$= x \log \left(5\right) - 4 \log \left(5\right)$

Subtract $x \log \left(5\right)$ from both sides to get:

$x \left(\log \left(7\right) - \log \left(5\right)\right) = - 4 \log \left(5\right)$

Divide both sides by $\left(\log \left(7\right) - \log \left(5\right)\right)$ to get:

$x = \frac{- 4 \log \left(5\right)}{\log \left(7\right) - \log \left(5\right)} \approx - 19.133$


text:
# Polyurethane glues?

### Help Support HomeBuiltAirplanes.com:

#### Mike.Smith

##### Member
Are polyurethane glues like Gorilla Glue suitable for any aspects of aircraft construction? I have used it with great success building furniture, but of course airplanes are not furniture.

#### George Sychrovsky

##### Banned
The gorilla glue is the same stuff as the expanding insulation foam for filling cracks and gaps, its about as strong as dry gorilla snot

#### orion

##### Well-Known Member
To interject a translation of the above - not very.

The polyurethane has the same basic properties as Clark-Foam, the material commonly used for surfboards. It ends up with a brittle, fryable surface (it damages easily) and the whole makup of the glue ends up being realtively susceptible to shock and vibration, at which point it just disintegrates and comes apart.

It's use on parts that are not subject to repeated loads and/or vibration is OK, but of course that's not an airplane.

#### Falco Rob

##### Well-Known Member
"Are polyurethane glues like Gorilla Glue suitable for any aspects of aircraft construction?"

Absolutely - you can use them to build your workbench . . and nothing else.

#### Medic9204

##### Well-Known Member
What about Liquid Nails and stuff like that?

#### wally

##### Well-Known Member
The Liquid Nails would probably work ok on something like attaching foam ribs to plywood when building an ultralight. Other than that, no.

If you are thinking about trying to save  on glues when building something like a "real" airplane with a decent size engine, you aren't going to save much. The cost of glue for a wood airplane is a small percentage of the complete expense.

For wood, use T-88 epoxy or whatever the plans call for. You will sleep better at night knowing it won't be a failed glue joint that "bites" you.

Oh, are you asking what liquid nails is made of? Just re-read your post. I think it is an organic adhesive refered to generally as mastic. I am sure someone else will know.
Good luck,
Wally

#### Falco Rob

##### Well-Known Member
Wally is right on the money.

To put things into perspective -

The cost of glue as a percentage of the overall cost of an aircraft is miniscule - probably about 0.5% (about $500 in$80K in my case)

Considering that your very life may depend on it there doesn't seem to be a good arguement for skimping on it.

Money can be saved in lots of inventive ways, but cost cutting on structural issues can lead to a world of hurt.

#### Medic9204

##### Well-Known Member
Money isn't really a concern for me. I'm more looking at availablity and ease of use. I don't think you can get T-88 at the hardware store.

What does anyone think about Aircraft Spruce's "All-Purpose Structural Adhesive?" It claims "similar" properties to T-88 but is available in a slower gel time (up to 2.5 hours). Is there any disadvantge to this product in the end result?

Wilke

#### Medic9204

##### Well-Known Member
Dried gorilla snot

How stong IS dried gorilla snot, anyway?

#### Falco Rob

##### Well-Known Member
In response to your second post - you don't see many gorilla's with their finger glued up their nose (well . . . not forever, anyway) so I guess the answer is - "not very" !

Back to the subject of glue - Have you considered West Systems epoxy?

I'm using it for exactly the reasons you've quoted - it's very user friendly and it's readily available (even in Aust).

The primary reason for my choice however is that it was specifically designed as a wood adhesive, not a general purpose glue.

#### org

##### Well-Known Member
I've used T88, APCO, resorcinol, and West System epoxy as glue at different times. They all work well, with resorcinol being the most critical of conditions and fit of parts.

The APCO you ask about is easy to use and shares the T88's tolerance for temperature, and is cheaper to boot. I've always liked it.

Right now I use West System. It's not as viscous as the others, but can be thickened by adding SMALL amounts of colloidal sylica. West seems to be pretty available locally at least in larger metro areas. For me, the West is easier to work with and makes for an easier cleanup of squeezed out glue. Since it has several hardeners it can be used for glueing, laminating of fiberglass, and protective coating.

Your mileage may vary so far as ease of use is concerned, but if you use good techniques, I think any of the epoxies mentioned will do a good job for you.

Olen

#### Bluerooster

##### Member
Epoxy or Resorcinol. According to AC 43.13.1b Resorcinol is the only approved adhesive. But the Epoxy adhesives are mentioned as being acceptable. Resorcinol requires the parts to fit very tightly, with no sanding to fit.