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homogenous

▪ I. homogenous, a. (həʊˈmɒdʒɪnəs) [f. homo- + Gr. γένος race + -ous.] 1. Biol. = homogenetic 1.1870 Ray Lankester in Ann. Nat. Hist. VI. 36 Structures which are genetically related, in so far as they have a single representative in a common ancestor, may be called homogenous. We may trace an homoge... Oxford English Dictionary

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Homogenous Society: Definition and Examples (2024) - Helpful Professor

Oct 23, 2023A homogenous society is one where people share a largely similar outlook. In these societies, there is one dominant way of thinking and acting, which is shared by most people. Homogeneity in cultures is often the result of geographical isolation, shared cultural history, or government policies. Examples include Japan, Native American Tribes ...

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Linear algebra: What is the difference between homogenous and ...

Particular solution - any specific solution to the system. The question from the book: Suppose that MX=V is a linear system, for some matrix M and some vector V. Let the vector P be a particular solution to the system and the vector H a homogeneous solution to the system. Which of the following vectors must be a particular solution to the system?

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Homogenous diff equations of the form P(x,y)dx + Q(x,y)dy = 0 thank you for taking the time to help me out. I am reviewing a past test while looking in my book to try to figure out how to do this. I understand the way...

Based on my research session (aka studying for finals), I finally found a source that put it this way: A function G(x,y) is homogenous of degree n if: y with $\lambda x$ and $ \lambda y$ You yield the same function being multiplied by some power of lambda ($\lambda^n$) then you know the equation is homogenous

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Homogeneous coordinate representation of a vertical line Is there homogenous coordinate representation for a vertical line passing through an arbitrary point on the x axis (say C). Generally this is represented as: ...

Two ways to tackle this. 1. Using the equation. The equation of a line with vector $[a:b:c]$ is $ax+by+cz=0$ in homogeneous coordinates. If the plane is embedded at $z=1$ that's $ax+by+c=0$ in affine coordinates. Now you can write your $x=C$ as $1x+0y-C=0$ and obtain coordinates $[1:0:-C]$ for the l...

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Why are all homogenous systems consistent? A linear system of form $A\vec{x}=\vec{0}$ is called homogeneous. Why are all homogenous systems consistent?

A system is defined as inconsistent if its row-reduced echelon form contains a row of form $\begin{bmatrix} 0 & 0 & 0 & ... & 0 & | & k \end{bmatrix}$ where $k \neq 0$ and | is a separator within augmented matrix. Since your system equals $\vec{0}$, it is impossible to have $k \neq 0$, rendering the...

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Does Euler's homogenous function theorem hold for functions homogenous in some of its independent variables? All proofs of Euler's homogenous functions theorem I've come across seem to assume the function is homogenou...

Yes. If a function is _weighted homogeneous_ , namely, if there are positive integers $q_1, \dots, q_n, d$ such that \begin{align} \lambda^{d} f(z_1,\dots,z_n) = f(\lambda^{q_1} z_1, \dots, \lambda^{q_n} z_n), \end{align} then it satisfies the _weighted Euler equation_ , \begin{align} d f = \sum_{i ...

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A homogenous polynomial of degree $k$. $f: \mathbb R^n \to \mathbb R$ is a smooth map such that $f(rv)=r^kf(v)$ for all $v\in \mathbb R^n$ and $r\in\mathbb R$. So $f$ has to be a homogenous polynomial of degree $k$? ...

Now if $f \neq 0$ taking into account that $P(rx)= r^k P(x)$, one can easily conclude that $P$ has to be a homogenous polynomial of degree $k$

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Construction of Homogenous Differential Equation We have to construct a homogenous differential equation of second order which has y(t) = e^t cos(t) as solution. I know have some knowledge of how to solve (some) diff...

Derive. $$y'(t)=e^t\cos t-e^t\sin t=y(t)-e^t\sin t,$$ $$y^{''}(t)=y'(t)-e^t\sin t-y(t).$$ Then subtracting the second equation from the first you arrive at $$2y'(t)-y^{''}(t)-2y(t)=0.$$

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Suppose $p(x , y) = ax^2 + bxy + cy^2$ is a homogenous real polynomial Suppose $p(x , y) = ax^2 + bxy + cy^2$ is a homogenous real polynomial of degree $2$ such that $b^2 < 4ac$, and $q(x , y)$ is a homogenous real po...

Assume WLOG that $a, c > 0$ and pick $\epsilon > 0$ so small that $(a-\epsilon)(c-\epsilon) > b^2$. Then for any $(x, y) \in \Bbb{R}^2$ we have $$ p(x, y) \geq \epsilon (x^2 + y^2). $$ (Or, if spectral theory is applicable, pick $\epsilon$ as the smaller of two positive eigenvalues associated to the...

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Help needed regarding homogenous equations in algebra. I have just started with algebra and I see here something about homogenous equations but I am just not able to figure it out. I read this answer here, Homogenou...

The book is saying that if $P(x,y,z)$ is homogenous then say if degree $k$, then $$P(ax,ay,az)=a^kP(x,y,z)$$ So multiplying the variables by a constant

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Question on homogeneous ideal in a graded ring In an $\Bbb{N}$-graded ring $R=\bigoplus_nR_n$, an element is called _homogenous (of degree $n$)_ if it is contained in $R_n$. An ideal is called _homogenous_ if it is ge...

$I$ is generated by homogeneous elements $f_1,…,f_s$. so $f=\sum_ig_if_i$. if $g_t$ were not homogeneous (for some t) use _associative_ property ($f_i$s may be Repeated). $\deg f-\deg f_i$, by definition of graded rings ($R_i R_j \subset R_{i+j}$). (in fact $\deg g_if_i=\deg g_i+\deg f_i = \deg f$, ...

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what will be the basic definition of homogenous equation for a novice? what will be the basic definition of homogenous equation for a novice? have already seen Definition of homogeneous ODE and dint get any wiser. hel...

The basic definition of homogeneous is that it makes no difference if you multiply every variable by some (nonzero) number $k$. If $f(x,y)$ is a function of two variables, then we'd call it "homogeneous" if $f(kx,ky) = k^df(x,y).$ In differential equations, the $d$ is usually 0. The function $f(x,y)...

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Concepts: time homogenous and independent increments Can someone give me an illustrative example for a time homogenous process without independent increments and for a process that is not time homogenous, but has inde...

First case: $X_n=(-1)^nU$ with $U$ symmetric, not deterministic. In continuous time, $X_t=\cos(t+2\pi V)$ with $V$ uniform on $(0,1)$. Second case: $X_n=x_n$ with the sequence $(x_n)$ deterministic and not constant. In continuous time, $X_t=x_t$ with the function $x:t\mapsto x_t$ deterministic and n...

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Degree 0 rational function on unit sphere. Suppose I have a degree zero homogenous rational function which has constant value on unit sphere. Does it mean it has constant value over $\mathbb R^n- 0$? If yes, why? By a...

Yes it does. If $x$ is in $\mathbb{R}^n - \\{0\\}$, then $$ \frac{P(x)}{Q(x)} = \frac{P(\lambda v)}{Q(\lambda v)}, $$ where $\lambda = \| x \|$ and $v = x/ \|x\|$. Since $P$ and $Q$ are both homogeneous, say of degree $d$, $$ \frac{P(x)}{Q(x)} = \frac{P(\lambda v)}{Q(\lambda v)} =\frac{\lambda^d}{\l...

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homogenous

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homogenous

Homogenous Society: Definition and Examples (2024) - Helpful Professor

Linear algebra: What is the difference between homogenous and ...

Homogenous diff equations of the form P(x,y)dx + Q(x,y)dy = 0 thank you for taking the time to help me out. I am reviewing a past test while looking in my book to try to figure out how to do this. I understand the way...

Homogeneous coordinate representation of a vertical line Is there homogenous coordinate representation for a vertical line passing through an arbitrary point on the x axis (say C). Generally this is represented as: ...

Why are all homogenous systems consistent? A linear system of form $A\vec{x}=\vec{0}$ is called homogeneous. Why are all homogenous systems consistent?

Does Euler's homogenous function theorem hold for functions homogenous in some of its independent variables? All proofs of Euler's homogenous functions theorem I've come across seem to assume the function is homogenou...

A homogenous polynomial of degree $k$. $f: \mathbb R^n \to \mathbb R$ is a smooth map such that $f(rv)=r^kf(v)$ for all $v\in \mathbb R^n$ and $r\in\mathbb R$. So $f$ has to be a homogenous polynomial of degree $k$? ...

Construction of Homogenous Differential Equation We have to construct a homogenous differential equation of second order which has y(t) = e^t cos(t) as solution. I know have some knowledge of how to solve (some) diff...

Suppose $p(x , y) = ax^2 + bxy + cy^2$ is a homogenous real polynomial Suppose $p(x , y) = ax^2 + bxy + cy^2$ is a homogenous real polynomial of degree $2$ such that $b^2 < 4ac$, and $q(x , y)$ is a homogenous real po...

Help needed regarding homogenous equations in algebra. I have just started with algebra and I see here something about homogenous equations but I am just not able to figure it out. I read this answer here, Homogenou...

Question on homogeneous ideal in a graded ring In an $\Bbb{N}$-graded ring $R=\bigoplus_nR_n$, an element is called _homogenous (of degree $n$)_ if it is contained in $R_n$. An ideal is called _homogenous_ if it is ge...

what will be the basic definition of homogenous equation for a novice? what will be the basic definition of homogenous equation for a novice? have already seen Definition of homogeneous ODE and dint get any wiser. hel...

Concepts: time homogenous and independent increments Can someone give me an illustrative example for a time homogenous process without independent increments and for a process that is not time homogenous, but has inde...

Degree 0 rational function on unit sphere. Suppose I have a degree zero homogenous rational function which has constant value on unit sphere. Does it mean it has constant value over $\mathbb R^n- 0$? If yes, why? By a...