Recent content by Mark Harder
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Undergrad Chiral symmetries in E[SUP]^n[/SUP]
As a biochemist, I deal with chirality of molecules all the time. If you have a tetrahedral molecule, for example a carbon atom, and all 4 vertices are labeled differently, as in different atoms on each one, then that molecule has a mirror-symmetric one that cannot be superimposed on the...- Mark Harder
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- Chiral Chirality Euclidean geometry Symmetries Triangles
- Replies: 1
- Forum: General Math
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Undergrad Does topology distinguish between real and imaginary dimensions?
As I understand topology, any two objects that can be transformed to each other by a continuous function are 'identical' in the sense that their images can be superimposed on each other. If you can write a function that maps one of your tori one-to-one onto another one, then the two are...- Mark Harder
- Post #10
- Forum: Topology and Analysis
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InWhat Situations Do We Enounter the Golden Ratio?
One of the roots of ##x^2 -x -1## is ## \frac {1 + \sqrt 5} 2 ## and that = ## \Phi ## .- Mark Harder
- Post #8
- Forum: Precalculus Mathematics Homework Help
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Why Does Positive Charge Exert Elec. Field Beyond Neg. Charge?
Lucky, By placing opposite charges near each other you have created an electric dipole. It's field will look similar to that of a magnetic dipole. It will extend throughout space, but its strength will fall off as a higher power with distance than 1/r^2. 1/r^6? I forget what power exactly...- Mark Harder
- Post #15
- Forum: Introductory Physics Homework Help
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Engineering Differential amplifier confusion (BJTs + Operational Amp)
Dammit, I posted a long answer, but PF seems to have deleted it. The short answer is that all of Is flows through the left transistor because you are trying to keep its base at 2V when it tries to stay at 0.7 V above common (what you mean by ground in your circuit). A transistor is a...- Mark Harder
- Post #37
- Forum: Engineering and Comp Sci Homework Help
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Disproving a statement about whole numbers
Proof by contradiction is overly complicated and you don't need to make any assumptions about a, n and m or break the proof into separate cases. The disproof derives from the facts that a is a natural number and so must be positive, while its factors n and m are drawn from the integers, which...- Mark Harder
- Post #16
- Forum: Math Proof Training and Practice
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Capacitance Questions: Troubleshooting Parallel Plate Capacitors
There are several things missing from your description of the experiment. Am I right in saying that the (ams) thing is a capacitance meter? What is the sensitivity of this device? Your theoretical calculation of the expected capacitance is 0.141 pico farads. That's an extremely small...- Mark Harder
- Post #20
- Forum: Electrical Engineering
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Is the 'Randomness' of Evolution Really Random?
I have no issue with your statement as far as it goes; but we must remember that mutations often result in a trade-off. Population A may be resistant to an antibiotic, for instance; but that mutation might also slow the growth and reproduction of A or cause it to use up more energy in order to...- Mark Harder
- Post #18
- Forum: Biology and Medical
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Why are natural products considered safe over conventional chemotherapy
I won't argue with the "very expensive" part. However, the rest of this analysis is self-contradictory, IMO. Mono-targeting drugs are exactly those that produce fewer side effects, all other things being equal. It's the affinities of multiple targets for a pharmaceutical that are likely to...- Mark Harder
- Post #23
- Forum: Biology and Medical
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Why are natural products considered safe over conventional chemotherapy
This reference is from an advocacy organization promoting certain ideas about herbal cancer treatments, not a peer-reviewed report of research into the subject. I gave up reading when I realized that it is a compendium of opinions, not observations.- Mark Harder
- Post #22
- Forum: Biology and Medical
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Is the 'Randomness' of Evolution Really Random?
It's true that there are a lot of repeating sequences, sometimes known - erroneously or not - as 'junk' DNA and presumably mutations in such sequences would be silent. Assuming, that is, the mutated sequence truly has no sequence-sensitive function. Last I heard, this question has not been...- Mark Harder
- Post #16
- Forum: Biology and Medical
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High pitched noise with some elctronics
Yep, the snakes are venomous, but those said-to-be-delicious venom glands, they're poisonous.- Mark Harder
- Post #18
- Forum: Electrical Engineering
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High pitched noise with some elctronics
WTH? All reptiles are protected in Australia? All reptiles in Australia are deadly venomous, mate. Including the tiger snake, BTW. As are all spiders, and those platypuses with venomous spines on their rear legs. Or else they're going to eat you and tuck you under a log underwater, like the...- Mark Harder
- Post #15
- Forum: Electrical Engineering
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Why isn't tungsten used in nuclear reactors?
Your description of the cultural factors at work at Fukushima reminds me of the recent docudrama, "Chernobyl". According to my interpretation, the Soviet system was responsible for the resistance to accepting the truth about the accident, right down to fundamentals like, Did the reactor...- Mark Harder
- Post #19
- Forum: Nuclear Engineering
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High pitched noise with some elctronics
Do you hear the noise when you use a battery-powered device? All the devices you mentioned are powered by line voltage, I think.- Mark Harder
- Post #13
- Forum: Electrical Engineering