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From: Ray Koopman on 15 Feb 2010 19:28
On Feb 15, 2:31 pm, icystorm <icyst...(a)hotmail.com> wrote:
> Ray, that looks like a pretty good solution. The only thing further
> that I did, and correct me if I am wrong, is add a range for i (i=0
> below sigma and 25 above sigma).
>
> Is it valid (e.g., legal) to define a total possible range for i when
> i exists in multiple sets? Also, do you find the result to be 3, after
> considering the four variables declared in the example (posted below)?
>
> http://www.box.net/shared/kkq9xpi2d5
>
> Thanks!
>
> J

The first "i" in sum_i [x1_i <= R34e] + ... was a subscript
on the summation sign, not a multiplier on [x1_i <= R34e].

No, you don't need an explicit range for i. In fact, it would be
misleading because each list has a different number of elements.
(And remember that there is no more i=0.)

It would be legal to omit the i subscript on x1, x2, x3, x4
in the headers of the tables.

>
> On Feb 15, 2:33 pm, Ray Koopman <koop...(a)sfu.ca> wrote:
>> On Feb 15, 9:36 am, icystorm <icyst...(a)hotmail.com> wrote:
>>>
>>> I thought of an easy way to remove the necessity of having y variables
>>> present in set, assuming that the sigma notation rules allow one to
>>> sum the FLOOR of each INDEX (e.g., [i],[j],[k],[m]) across multiple
>>> sets.
>>>
>>> Is my intent clear in the following example and is it all "legal"?
>>>
>>> http://www.box.net/shared/3p9rbciph0
>>>
>>> Thanks!
>>>
>>> J
>>
>> "Floor" truncates non-integer values: floor(2.5) = 2, floor(2) = 2.
>> You want "Iverson brackets", which give 1 or 0 according
>> as the statement inside the brackets is true or false.
>> Then delete row 0 in all the tables, and you can write
>>
>> sum_i [x1_i <= R34e] + [x2_i <= R50e] + [x3_i <= R64e] + [x4_i <=
>> R87e].
>>
>> But you need the plus signs. Commas would have no meaning.
From: icystorm on 15 Feb 2010 20:07
On Feb 15, 6:28 pm, Ray Koopman <koop...(a)sfu.ca> wrote:

> The first "i" in  sum_i [x1_i <= R34e] + ...  was a subscript
> on the summation sign, not a multiplier on [x1_i <= R34e].
>
> No, you don't need an explicit range for i. In fact, it would be
> misleading because each list has a different number of elements.
> (And remember that there is no more i=0.)
>
> It would be legal to omit the i subscript on x1, x2, x3, x4
> in the headers of the tables.

Here is the latest change, per your recommendations, Ray.

http://www.box.net/shared/6y6z04zmq4

Three questions:

1. When you said "subscript of the summation sign" did you mean that
the i should be placed directly beneath sigma (as shown in the new
example)?

2. I removed the i subscripts from the column headers, as you
suggested, but I should leave the i subscripts in the conditional
terms within the Iverson brackets to the right of sigma, because the i
subscripts there refer to the i subscript below sigma, correct?

3. In the problem shown in the new example, did you find that the
summation of all positive conditions equals 3?

Thanks kindly for you assistance and patience!

J


From: Ray Koopman on 15 Feb 2010 20:32
On Feb 15, 5:07 pm, icystorm <icyst...(a)hotmail.com> wrote:
> On Feb 15, 6:28 pm, Ray Koopman <koop...(a)sfu.ca> wrote:
>
>> The first "i" in sum_i [x1_i <= R34e] + ... was a subscript
>> on the summation sign, not a multiplier on [x1_i <= R34e].
>>
>> No, you don't need an explicit range for i. In fact, it would be
>> misleading because each list has a different number of elements.
>> (And remember that there is no more i=0.)
>>
>> It would be legal to omit the i subscript on x1, x2, x3, x4
>> in the headers of the tables.
>>
> Here is the latest change, per your recommendations, Ray.
>
> http://www.box.net/shared/6y6z04zmq4
>
> Three questions:
>
> 1. When you said "subscript of the summation sign" did you mean that
> the i should be placed directly beneath sigma (as shown in the new
> example)?

Yes.

>
> 2. I removed the i subscripts from the column headers, as you
> suggested, but I should leave the i subscripts in the conditional
> terms within the Iverson brackets to the right of sigma, because the i
> subscripts there refer to the i subscript below sigma, correct?

Yes.

>
> 3. In the problem shown in the new example, did you find that the
> summation of all positive conditions equals 3?

Yes.

>
> Thanks kindly for you assistance and patience!
>
> J

One more thing: the brackets ahould be upright, like the + and <= ,
not slanted.
From: icystorm on 15 Feb 2010 21:13
On Feb 15, 7:32 pm, Ray Koopman <koop...(a)sfu.ca> wrote:
> On Feb 15, 5:07 pm, icystorm <icyst...(a)hotmail.com> wrote:
>
>
>
>
>
> > On Feb 15, 6:28 pm, Ray Koopman <koop...(a)sfu.ca> wrote:
>
> >> The first "i" in  sum_i [x1_i <= R34e] + ...  was a subscript
> >> on the summation sign, not a multiplier on [x1_i <= R34e].
>
> >> No, you don't need an explicit range for i. In fact, it would be
> >> misleading because each list has a different number of elements.
> >> (And remember that there is no more i=0.)
>
> >> It would be legal to omit the i subscript on x1, x2, x3, x4
> >> in the headers of the tables.
>
> > Here is the latest change, per your recommendations, Ray.
>
> >http://www.box.net/shared/6y6z04zmq4
>
> > Three questions:
>
> > 1. When you said "subscript of the summation sign" did you mean that
> > the i should be placed directly beneath sigma (as shown in the new
> > example)?
>
>   Yes.
>
>
>
> > 2. I removed the i subscripts from the column headers, as you
> > suggested, but I should leave the i subscripts in the conditional
> > terms within the Iverson brackets to the right of sigma, because the i
> > subscripts there refer to the i subscript below sigma, correct?
>
>   Yes.
>
>
>
> > 3. In the problem shown in the new example, did you find that the
> > summation of all positive conditions equals 3?
>
>   Yes.
>
>
>
> > Thanks kindly for you assistance and patience!
>
> > J
>
> One more thing: the brackets ahould be upright, like the + and <= ,
> not slanted.- Hide quoted text -
>
> - Show quoted text -

Thanks! I will make that change. One final thing: I visited your web
page at SFU. I would like to cite your assistance here in the
acknowledgements section of a paper I am writing. Do you have a
preference for citations, such as a title, etc.?

Thanks again!

Cheers,
J
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