Create indexed solution lists with Do Command

When I run this code, why don't I produce lists called roots [j] that each contain 3 elements that are the roots of the equation?

For example, if I enter roots [0], I get roots [0] as an answer instead of 3 different roots.

Do[roots[a] = z/.NSolve[z^3 + 3 z^2 - z == a, z]], {a, -15, 
15, 0.1}];

Note: I asked a similar question some time ago and it was closed when I made a typo. This is the right code that is not working for some reason. I still don't understand why when I write roots [2.4] I don't get the 3 roots in a list.

Tensors – How does Indexed work with the sparse array?

I want to use indexed because it's an element (0.500), but I'm not sure how to write it without getting a format error or tensor error.

(CapitalDelta)t = .0001;
t = .0833;
(Sigma) = .2183;
(CapitalDelta)s = 5;
s = (0, 500);
(Mu) = (((Sigma)^2 Indexed(s, i)^2)/
    Indexed((CapitalDelta)s, i)^2*(CapitalDelta)t);
(Alpha) = (Indexed(s, i)/(
   2*Indexed((CapitalDelta)s, i)^2*(CapitalDelta)t));
cn1(k2_, n_) = 
 SparseArray({{m_, m_} -> 
    1/2 + 1/2*(Mu) + 
     1/2*Indexed(rate, {k2, n})*(CapitalDelta)t, {m_, l_} /; 
     l - m == 1 -> -(1/4)*(Mu) - 
     1/2*Indexed(rate, {k2, n})*(Alpha), {m_, l_} /; 
     m - l == 1 -> -(1/4)*(Mu) + 
     1/2*Indexed(rate, {k2, n})*(Alpha)}, {101, 101})

ct.category theory – categorical structure required for internal aggregations (e.g. cardinality, indexed sums / products)?

Consider a category $ mathcal {C} $ contains a natural number object mathbb {N} as well as objects and arrows $ X overset {p} { leftarrow} Y overset {f} { rightarrow} mathbb {N} $, We are often interested in one $ mathbb {N} $-Value up $ X $ by "folding" over the fibers of $ Y $, Write $ Y_x: = p ^ {- 1} (x) $Some examples include

Map($ X $): $ 1 leftarrow X overset {! 1} { to} ( mathbb {N}, +) $

Total($ f: X to mathbb {N} $): $ 1 leftarrow X overset {f} { to} ( mathbb {N}, +) $

Prod ($ f: X to mathbb {N} $): $ 1 leftarrow X overset {f} { to} ( mathbb {N}, times) $

Although these values ​​are determined canonically, they do not (generally) define global elements $ 1 to mathbb {N} $ in the $ mathcal {C} $, The easiest way to recognize this is to note that global elements must be preserved through natural transformations between presheaves, but cardinality, etc., does not.

Question 1) What type of categorical structure is required to internalize fiber aggregations like the ones mentioned above?

Guess: We have to assume that $ mathbb {N} $ is an object classifier in internal theory. Then we can map $ X to mathbb {N} $ unique ($ x mapsto Card (Y_x) $) and an ambiguous one $ Y to mathbb {K} $ The resulting square becomes a pullback. Then we can extend $ f $ to $ mathbb {K} $ (e.g. expansion by zero or one) and define the aggregations using recursive definitions.

Question 2) What explains the failure of the naturalness of these aggregates? Does it arise from the use of a universe or does it possibly indicate a hidden dependency on Heyting / dependent product structures? Is there a weakening or generalization of naturalness that still applies to these more general arrows?

References for this and related topics are very much appreciated.

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SQL Server – Do filtered indexed views cause conflicts in the underlying table if rows are added to the table that are outside the filter?

If I create an indexed view on a spreadsheet and the query for that spreadsheet contains a filter, new records are added to the spreadsheet that do not fall into that filter (and therefore are not displayed in the indexed view), adding additional competition from the indexed view the table while these records are added to it?



SELECT TextColumn1, TextColumn2
FROM dbo.BoringTable
WHERE DateColumn1 < '1/1/2019';

CREATE CLUSTERED INDEX IX_FilteredIndexView_DateColumn1 ON FilteredIndexView (DateColumn1);

INSERT INTO dbo.BoringTable (TextColumn1, TextColumn2, DateColumn1)
SELECT 'SomeText', 'SomeOtherText', '12/11/2019'; -- Some date that falls outside the filter of the indexed view

With Solr 4.9, Drupal7 attachments can not be indexed and searched

After setting up server and index (Attachment: File field has been added), I am able to search and query, except description of D7 content Appendix (Neither Title nor Content) from the Solr panel in the browser.
Other documents and videos recommend indexing and searching attachments without tinkering with Tika,
Please suggest a solution.
Env: Solr 4.9.1 and Drupal 7
D7 installed and activated modules:
Search API: 7.x.
Search attachment: 7.x
Apache Solr Access: 7.x

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