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| bio | website | |
|---|---|---|
| location | Albany, CA | |
| age | ||
| visits | member for | 1 year, 1 month |
| seen | 4 hours ago | |
| stats | profile views | 2,023 |
If I see further than most, it is because I have stood on the toes of giants and they kicked me high into the air...
However, there is nothing to suggest that I see further than most.
I am (inasmuch as one 'is' an occupation) an engineer. My mathematical skills are rather pedestrian, with a rare insight every now and then. I have been lucky enough to sit in the same room with some famous mathematicians & engineers. My Erdős number is 5, which undoubtedly makes me as unique as an Irishman in a pub. And I have been spotted in The Pub from time to time.
In professional circumstances, my value add has usually been the injection of common sense and completion of grunt work when perspectives and energies are unfocused.
Current age is a two digit number divisible by the cardinality of a pack of cards.
My real name is Joe Higgins. Apparently, my last name means 'of the Viking' in Irish.
I can be reached at joe dot higgins at gmail dot com.
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6h |
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function property What is the question? |
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6h |
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Function generation by input $y$ and $x$ values I am guessing you swapped your $x$ and $y$ above. If so, and the $x$ values are evenly spaced, you could use a scaled version of the Bernstein polynomials... |
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15h |
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Rouché Theorem to calculate the number of zeros I need more caffeine. I am showing $f$ and $g$ have the same zero count, your version shows $f$ and $f+g$ have the same zero count. |
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15h |
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Rouché Theorem to calculate the number of zeros Thanks, I can't count! |
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15h |
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Rouché Theorem to calculate the number of zeros I believe you need to show something like $|f(z)+g(z)| < |f(z)|$ to apply Rouché? |
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1d |
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Properties of Continuous Functions What about $f(x) = x^2$, with $c=1$? |
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1d |
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Finding convex conjugate of a bounded function Following Rockafellar, you can let $g$ be the function that agrees with $f$ on $\operatorname{ri}( \operatorname{dom} f)$, and $+\infty$ elsewhere. Then $f^* = g^*$ where $f^*$ is as above, and $g^*$ is taken as the $\sup$ over $\mathbb{R}^n$. Choosing different $X$ is tantamount to changing $f$. Given this, I would imagine that it would be hard to find a general principle for selecting $X$ that is independent of your application? |
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1d |
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Fastest Algorithm for NLP with linear constraints This is not a quadratic program because of the square root. |
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2d |
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inner product (real or imaginary?) $(x,z) \mapsto \overline{x} z$ (possibly conjugate, depending on how you like your inner product) is an inner product on $\mathbb{C}$. Hence it is not necessarily real. |
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May 20 |
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Bounded sequence in Hilbert space contains weak convergent subsequence There is a short proof using Banach Alaoglu... |
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May 19 |
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Linear Regression: Expectation Proof Perhaps you meant $\beta_i E X_i$? Your question needs some context... |
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May 19 |
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Why is 987654321/123456789 = 8.0000000729? 8.000000072900000663390006036849054935326399911470239194379176... |
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May 19 |
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Why is a CDF right-continuous at “a” in [a,b), when property Pr(a<X≤b) doesn't even require point “a” to exist, and “b” could carry baggage? By not existing do you mean that $a$ is not in the range of $X$? Right continuity follows from the properties of measure, since we have $\cap_n (-\infty,b+\frac{1}{n}] = (-\infty,b]$. |
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May 15 |
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Taylor Expansion of Power Series This is the mean value theorem, generalized to a higher derivative. (See Taylor's theorem with Lagrange's form of the error.) |
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May 15 |
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To show that $\sqrt{z^2-1}=\exp(\frac{1}{2} \log(z^2-1))$ is analytic in the plane minus [-1,1] See math.stackexchange.com/questions/166854/… |
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May 14 |
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Equivalent norms and isometries +1 Nice approach. |
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May 14 |
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Find function with given properties Correct, the proof does not rely on any smoothness hypotheses. (However, a convex or concave function defined on $\mathbb{R}$ can be shown to be continuous.) |
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May 14 |
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Find function with given properties By assumption $g(x_2)-g(x_1) >0$ and $x_2-x_1 >0$, so if $x \to -\infty$, then $x \frac{g(x_2)-g(x_1)}{x_2-x_1} \to - \infty$. |
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May 13 |
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Derivatives of trigonometric functions The suspense is killing me... |
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May 13 |
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is this function injective? In fact any function $n \mapsto (n,\text{whatever})$ must be injective. |
