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heartily

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heartily
heartily, adv. (ˈhɑːtɪlɪ) [f. hearty a. + -ly2. Cf. also heartly adv.] In a hearty manner. 1. With full or unrestrained exercise of real feeling; with genuine sincerity; earnestly, sincerely, really; with goodwill, cordially.a 1300 Cursor M. 20054 Qua hertili hers or redis it. c 1385 Chaucer L.G.W. ... Oxford English Dictionary
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heartily
heartily/ˈhɑ:tɪlɪ; `hɑrtɪlɪ/ adv1 with obvious enjoyment and enthusiasm; vigorously 尽情地; 热心地; 痛快地 laugh, sing, eat, etc heartily 开怀大笑、 纵情歌唱、 大吃特吃.2 very; truly 极其; 确实: be heartily glad, pleased, relieved, upset, etc 极其高兴、 愉快、 轻松、 不安等 I'm heartily sick of this wet weather. 我非常讨厌这种潮湿的天气. 牛津英汉双解词典
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Travis Kelce was heartily booed by Mavericks fans while ...
12 hours ago — Travis Kelce doesn't have many fans within the Dallas Mavericks crowd, it seems. On Sunday, Kelce and Kansas City Chiefs teammate Patrick ...
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Churiyamai
The drivers worship this Goddess heartily. The name of the VDC and School is called Churiya hill. wikipedia.org
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Bezout's theorem extension (regarding uniqueness of x,y and converse). In my book Bezout's theorem is given as: **If a,b are integers, not both zero, then GCD(a,b) exists and there exist integers x and y such that (a...
For 4: if $(x,y)$ is a solution to $gcd(a,b) = ax + by$, then $(x+nb,y-na)$ is a solution as well for any whole number $n$. For 5: (reverse Bezout) Note that it is _not_ true that if $z = ax + by$, then $z = gcd(a,b)$. It _is_ true, however, that if $z = ax + by$, then $z = n*gcd(a,b)$ for some whol...
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How to associate median with angles?? I have got an olympiad problem which is like follow: In triangle ABC,let D be the midpoint of BC.If ∠ADB=45 and ∠ACD=30 ,determine ∠BAD. The main problem with the question is th...
Hint: note that $\widehat{CAD} = 15^\circ $ and $\widehat{ABD} + \widehat{BAD} = 135^\circ$. Apply the sine law twice to get: $$\frac{AD}{CD} = \frac{\sin 30^\circ}{\sin 15^\circ} = \frac{\sin(135^\circ -\widehat{BAD})}{\sin \widehat{BAD}} $$
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Lebesgue integral of $\frac{1}{\|\boldsymbol{x}-\boldsymbol{r}\|^2}$ on an infinite cylinder Let $V\subset \mathbb{R}^3$ be a solid infinite cylinder, or cylindrical shell, and let $\boldsymbol{r}\in\mathbb{R}^3\setmi...
We may assume WLOG that the (empty) cylinder is given by $x^2+y^2=1$ and the point $r$ lies on the positive $x$-axis at a distance $r$ from the origin. The integral is so given by: $$ \int_{-\infty}^{+\infty}\iint_{x^2+y^2=1}\frac{1}{(r-x)^2+y^2+z^2}\,dx\,dy\,dz=\iint_{x^2+y^2=1}\frac{\pi}{\sqrt{(r-...
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大快朵颐 [大快朵頤] - to gorge oneself, to eat heartily (idiom) - dà kuài duǒ ...
English - Chinese Dictionary | Meaning of 大快朵颐 [大快朵頤] in English: to gorge oneself, to eat heartily (idiom) | ChinesePod.com
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Can I apply Induction here ?? I have got a question Which is as follow: **If there are n participants in a knockout tournament then prove that (n-1) matches will be needed to declare a champion**. If I prove this pr...
Yes, you can use induction on $n$ to prove: $P(n)$: If there are $n$ participants in a knockout tournament, then $(n-1)$ matches will be needed to declare a champion. Base case(s): Is $(P(1)$ true? Sure: $P(1)$ If there is only one team ($n=1$), then no matches are needed $(n-1 = 1-1=0),$ because by...
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Evaluate $\int_0^1 \frac{1}{\sqrt x+\sqrt {(1-x)}}dx$ Evaluate $I=\int_0^1 \frac{1}{\sqrt x+\sqrt {(1-x)}}dx$. I applied $x=\sin^2\theta$,that makes $I=\int_0^{\pi/2} \frac{\sin2\theta}{\sin\theta+\cos\theta}d\theta$...
Hint: $$\sin2\theta=(\sin\theta+\cos\theta)^2-1$$ and $\sin\theta+\cos\theta=\sqrt2\sin\left(\dfrac\pi4+\theta\right)$ Use Integral of $\csc(x)$
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Should you accept the first correct response or the one with the most detail I just recently posted a question where I quickly received two correct responses. The first was posted a few minutes after I asked my questi...
Why_ behind the problem and solution hopefully encourages people reading it to learn more about their systems, and that's something we as a community heartily
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Lebesgue measure of a sphere While reading proofs (for ex. this) about measure theory I am inclined to think that it is implicitly intended that the $n$-dimensional Lebesgue measure of a hypersphere $\mathbf{S}^{n-1}$...
Suppose $\mu(S) > 0.$ Because $\mu(rE) = r^n\mu(E)$ for any measurable $E\subset \mathbb R^n$ and $r>0,$ we have $\mu(rS)\ge \mu(S)$ for $r\ge 1.$ Now $\\{1\le |x|\le 2\\},$ a compact subset of finite measure, contains the pairwise disjoint compact sets $S_k= (1+1/k)S, k = 1, 2, \dots $ This implies...
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How to estimate a linear function in $\mathbb R$, given rounded linearly spaced measurements? Given measurements $$\left \lfloor t+i\cdot x\right \rfloor \\\\\\\ i\in\left\\{ 0,1,\cdots ,N\right\\} \\\\\\\ x,t \in \ma...
I am going to assume $N$ is large and $x$ is small $(f(n-1)$ and $n_2$ be the last such $n$. Then $x\approx \frac{f(n_2)-f(n_1)}{n_2-n_1}$ and $t\approx f(0)+1-n_1x$.
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$\int_X f^p d\mu = p\int_{[0,+\infty)} t^{p-1}\mu(\{x\in X: f(x)>t\}) d\mu_t$ for any natural $p\ge 1$ Let $f:X\mapsto0,+\infty)$ be a non-negative measurable function defined on the space $X$, endowed with the comple...
Apply change of variables to the expression you have. You deduced that: $$\int_X f^p d\mu =\int_{[0,+\infty)} \mu(\\{x\in X: f(x)^p>t\\}) d\mu_t,$$ where $\mu(\\{x\in X: f(x)^p>t\\}=\mu(\\{x\in X: f(x)>t^{1/p}\\}$. Now substitute $t\mapsto t^p$ and the result follows because the derivative of this m...
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a doubt in finding distance in graph theory I was studying about a product graph which is defined as : !enter image description here. **I am taking $G_1$ and $G_2$ as connected graphs.** I found that for any 2 vert...
We do not need to assume $G_1,G_2$ connected. It is sufficient to assume that $G_1,G_2$ have no isolated vertices. Then for $(g,h),(g',h')\in V(G)$ pick $a\in G_1$ with $g\sim a$ and $b\in G_2$ with $h'\sim b$. Then $(g,h)\sim (a,b)\sim (g',h')$ shows that all distances in $G$ are $\le 2$ (and espec...
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