Successful culinary experiments
Ha ha! On Sunday, I made an excellent macaroni and cheese with porcini mushrooms, bacon, and panko breadcrumbs. I have to commit the blasphemy: this is much better than what my mom makes (or used to make before she effectively gave up cheese). I adapted this lighter recipe, replacing the milk with a mix of mushroom liquid, milk, and cream, adding mushrooms and bacon, and using a mix of gruyere and cheddar cheeses.
For the mornay sauce, I used a medium onion, 1/2 c. flour, a pint of heavy cream (which I originally acquired for the vaporware ginger cheesecake), a cup of the liquid from reconstituting the mushrooms, a cup of skim milk, 2 c. gruyere cheese, and 3 c. sharp cheddar. Reconstitute the mushrooms (I eyeballed it, no exact measurement: about as much mushrooms as bacon) and save some of the liquid for the bechamel. Cook the bacon and use the grease to saute the mushrooms. Chop the onion finely, saute in butter it until almost translucent: you don’t want it too cooked because … next you add the flour piecemeal and cook at the same heat for 4 minutes or so– I added chunks of butter as appropriate while adding in the flour, because this allowed me to be parsimonious with the initial amount of butter and helped me to avoid using more than necessary–, then add in the liquids and bring to a boil. Lower the heat and simmer until the sauce thickens. Now turn off the heat and fold in the cheese mixture.
Cook 1/2 lb. of noodles while doing all the above, until they’re tender (not al dente). Then fold in the cheese sauce, bacon, and mushrooms; add salt, pepper, and nutmeg to taste. Decant the mixture into a 9×9 pan– I lined mine with parchment paper so I didn’t have to deal with burnt-on sides and bottom, only the grease which leaked through. Melt a tablespoon of butter and mix in a cup of the breadcrumbs (and some parmesan if you have some), then sprinkle this mixture on top of the noodles. Bake in a 400 F oven until it’s done; I probably went about 40-50 minutes, but you should be able to say when from brownness or smell 
Next time, I’ll try adding in some basil (this time I only had arugula on hand, and that seems like a weird thing to put in mac and cheese), more mushrooms, experiment with cheeses (use Emmental if I can find it), and try cavatapi pasta. But that’ll be a while; this is way too fatty to eat often.
This is so rich that a small portion will fill you right up, so it could serve as a meal by itself. I was too tired after all that work to actually do it, but I imagined some simple roasted carrots would help diminish the uneasiness you might feel from eating a meal consisting entirely of lipids. At any rate, you’d want to pair this with something simple.
The second culinary experiment. Today I made my first smoothie on the level of Jamba Juice. The secret which made this smoothie so much better than my other attempts was simple: replace the ice with frozen pineapple chunks. So, the recipe is simple: frozen strawberries and frozen raspberries in equal amounts, slightly more frozen pineapple, and OJ. Blend it all together well, and enjoy: fruity and sweet. *Really* sweet, the way I like it, like Jamba Juice’s Caribbean Passion (or whatever it’s called); you can control this by varying the amount of pineapple, or adding ice. Any ideas for other sweetening agents? I’ll try mango, but I’m a little worried that it isn’t sweet enough.
I feel a bit guilty for making that tonight, because my dinner was roasted stone fruit– peaches, nectarines, plums, and randomly apples– with vanilla bean ice cream. I figured having ice cream for dinner isn’t bad if you add fruit and avoid eating anything else after that. I had to throw out one of the peaches– which sucked, because peaches turned out to be the only fruit that agreed with the ice cream– because it turned out to be rotten, and the roasting recipe turned out to be wack. (Incidentally, why is it that every time a recipe states a certain amount of time, I end up having to double or triple it to get the desired results?) So instead of the roasting process as I received and used it, I’ll give what I have extrapolated should give better results: slice your fruits into thin chunks, not so thin that they’ll get waterlogged when you roast them, or when you put them on the ice cream, but not so fat that the insides will be raw when the outsides are well roasted. Sprinkle 2-3 tablespoons of white sugar on them (I used 2 plums, 2 nectarines, 1 apple, and 1 peach; extrapolate) and just enough lime juice to get them wet (you really don’t want to use too much lime juice, or have any free at the bottom of the pan, because then everything will taste like lime– yuck). The only point of the lime juice is to prevent the fruits from oxidizing; toss the fruit to coat it, then bake in a preheated 400 F oven until caramelized; toss them when halfway done and swish the juices to keep from burning. Ideally you’ll get a nice sauce from the caramelized sugar and the fruit juices, and nice roasted flesh. Bowl your ice cream and put the hot fruit on top. I wonder what else you can eat these with.
Disappointing as the fruit turned out to be, the ice cream was still ice cream, so following it with smoothies was a bit much.
Possibly relevant posts:
- Indian cooking (9/14/2006)
- My favorite tuna recipe (2/7/2007)
- Goat cheese, arugula, and chorizo (9/14/2008)
it follows that 
That is, the spectral norm of a submatrix is smaller than the spectral norm of the matrix. Note that 
and its submatrices aren’t required to be square for this to hold.
to the full matrix? It is monotonic increasing, but what else can you say? Is there anything else you can say?
is invertible, 
and 
Show that 
and the norm is the usual spectral norm.![C[a,b]](/cz/latexrender/pictures/d930e3053f32dbc51f14e870df59674d.png "C[a,b]")
which converge pointwise to a function in the space converge weakly to the same limit. This was on one of my functional analysis exams here at Caltech, and I was not able to solve it without appealing to Radon measures. You can show this without taking that route– give it a shot!
a.e., 
and 
is bounded, then 
(weak convergence) in 
.
of the product space 
of measurable spaces 
is the smallest sigma algebra for which all the coordinate projections 
are measurable. That is, it is the sigma algebra generated by the sets 
According to 
where 
for all but finitely many 
where 
, but what if 
: 