## Is the Planeshifter’s “portal under their control” a fixed location or no?

About the portal, the prestige class demiplane seed ability (Manual of the Planes, p32) only says, “It has a single portal entry, which the planeshifter may control for access.”

What rules would be used to define the portal, and would it have to be fixed or can it be portable by whatever rules apply?

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## Halting problem for fixed Turing machine and fixed input

It is known that the halting problem is undecidable even when we fix either the Turing machine $$M$$ or the input $$w$$.

What if we fixed both the machine and the input? I.e., is it decidable for every fixed Turing machine $$M_0$$ and every fixed input $$w_0$$ that $$M_0$$ will halt on $$w_0$$ as input?

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## What counts as a “fixed range” spell for Persistent Spell?

The Persistent Spell feat in Player’s Guide to Faerûn allows a spell to last for 24 hours. The spell to be persisted must have a personal range or fixed range.

I’m having trouble finding a definition of ‘fixed range’ for a spell. One example given, detect magic, has a range of 60 ft. Are only spells with a non-variable range considered fixed?

Is a spell with range touch considered fixed? While the 3.0 Faerûn campaign setting errata specifically excludes touch spells, 3.5 makes no mention of this.

## Find the fixed point of a recursive functional?

A functional is a function which takes another function as a parameter.

The fixed point of a function is an input such that

F(x) = x 

Given an example functional,

T(F,x,y) = if x = 0 return 0            else return y + F(x - 1,y) 

what is the fixed point of the functional?

The functional looks similar to a recursive implementation of x * y given the if x = 0 return 0 and function call with x - 1, but I don’t see where to go with this. To find a fixed point in a normal mathematical equation you’d just set T(f,x,y) = f(x,y) and solve, but given the format that doesn’t really work. I can’t see how the RHS can be simplified to allow that.

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## Using a fix $key and variable$data vs partially variable $key with fixed$data in PHP’s hash_hmac()

This question was originally asked in stack overflow, but it was suggested to ask it here as well..

• not looking to improve on hash_hmac functionality. I’m rather interested in the $uri in the examples below.. The theory is that typically we create signed URI’s like $  superSecret = 'abc'; $data = 'https://localhost/verify/{user-id}/{email}';$  hash = hash_hmac('sha256', $data,$  superSecret);  $uri =$  data . '/?hash=' . $hash;  Then we can validate the signature by recreating a hash, and calling hash_equals(). If any of part of the data string changed, hash_equal() returns false. What happens if we switch some parameters around. This time instead of hashing different data, we hash the same data every time but with different keys. I.e. $  superSecret = 'abc' . $userId .$  email; $data = 'https://localhost/verify';$  hash = hash_hmac('sha256', $data,$  superSecret);  $uri =$  data; 

The above are dumbed down generalized examples. But I’m more interested in, is the concept correct? Would using different keys to hash the same data be as secure as using different data hashed by the same key.

Keep in mind that the ‘abc’ of $superSecret is never exposed. $ user-id and $email are concatenated onto the end of $ superSecret

The original question for those interested https://stackoverflow.com/questions/60401068/is-using-a-variable-key-with-constant-data-as-secure-as-using-a-constant-key-wit?noredirect=1#comment106850148_60401068

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## PTAS for Multiple Knapsack with Uniform Capacities, fixed number of Knapsacks

Consider the following problem:

We are given a collection of $$n$$ items $$I = \{1,…n\}$$, each item has a size $$0 < s_i \le 1$$ and a profit $$p_i > 0$$. There are $$m$$ (a fixed number) of unit-size knapsacks. A feasible solution is an $$m$$-tuple $$U=\{U_1,…,U_m\}$$, such that the size of items in each knapsack doesn’t exceed its capacity, and each item is packed in no more than one knapsack. more formally:

• for every $$j, 1 \le j \le m, U_j \subseteq I$$ and $$\sum_{i \in U_j}s_i \le 1$$
• for every $$j,l, 1 \le j < l \le m, U_j \cap U_l = \phi$$

the profit of the feasible solution is $$\sum_{j=1}^m\sum_{i \in U_j}p_i$$. The goal is to find a feasible solution of maximal profit.

I’m trying to show a PTAS for the problem.

It was suggested to use linear programming. I thought about the following (basic) linear program:

maximise $$\sum_{j=1}^m\sum_{i=1}^n x_{ij}p_i$$

under the constraints:

• for every $$1 \le j \le m \sum_{i=1}^n s_ix_{ij} \le 1$$ (the size of items in each knapsack doesn’t exceed its capacity)
• for every $$1 \le j \le n \sum_{j=1}^m x_{ij} \le 1$$ (each item is packed in no more than one knapsack).

I don’t know how to proceed from here. I’m not sure how to develop an algorithm (choose in which knapsack to put each item) based on this linear program. Can anyone pls give me a clue?

Thanks.

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## load local data on fixed width file inserting all columns with NULL values

Here is an example table with the load sql

DROP TABLE IF EXISTS exp_gpoper; CREATE TABLE exp_gpoper (   _id int(11) NOT NULL AUTO_INCREMENT,   date_updated datetime NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp(),   pun_county_num varchar(100) DEFAULT '',   pun_lease_num varchar(100) DEFAULT '',   pun_sub_num varchar(100) DEFAULT '',   pun_merge_num varchar(100) DEFAULT '',   company_number varchar(100) DEFAULT '',   company_name varchar(300) DEFAULT '',   PRIMARY KEY (_id),   KEY date_updated (date_updated),   KEY pun_county_num (pun_county_num),   KEY pun_lease_num (pun_lease_num),   KEY pun_merge_num (pun_merge_num),   KEY pun_sub_num (pun_sub_num),   KEY company_number (company_number),   KEY company_name (company_name) ) ENGINE=InnoDB DEFAULT CHARSET=latin1;  LOAD DATA LOCAL INFILE 'test.dat'  INTO TABLE exp_gpoper  (@_row)  SET pun_county_num = TRIM(SUBSTR(@row,1,3)),  pun_lease_num = TRIM(SUBSTR(@row,4,6)),  pun_sub_num = TRIM(SUBSTR(@row,10,1)),  pun_merge_num = TRIM(SUBSTR(@row,11,4)),  company_number = TRIM(SUBSTR(@row,15,7)),  company_name = TRIM(SUBSTR(@row,22,255)); 

Here is the content of the test.dat file:

001000000000000077777OTC USE                                                                                                                                                                                                                                                         003000000000000077777OTC USE                                                                                                                                                                                                                                                         003000567000000020011M & D PUMPING SERVICE INC                                                                                                                                                                                                                                       003000587000000022576SCOGGINS PRODUCTION LLC                                                                                                                                                                                                                                         003000588000000022576SCOGGINS PRODUCTION LLC                                                                                                                                                                                                                                         003000639000000017441CHESAPEAKE OPERATING LLC                                                                                                                                                                                                                                        003000963000000019694BVD INC                                                                                                                                                                                                                                                         003000964000000018119BLAKE PRODUCTION CO INC                                                                                                                                                                                                                                         003002207124830022281SANDRIDGE EXPLORATION AND PRODUCTION LLC                                                                                                                                                                                                                        003002394000000020891SUPERIOR OIL & GAS LLC                                                                                                                                                                                                                                           

This works fine:

DROP TABLE IF EXISTS exp_gpexempt; CREATE TABLE exp_gpexempt (   _id int(11) NOT NULL AUTO_INCREMENT,   date_updated datetime NOT NULL DEFAULT current_timestamp() ON UPDATE current_timestamp(),   pun_county_num varchar(100) DEFAULT '',   pun_lease_num varchar(100) DEFAULT '',   pun_sub_num varchar(100) DEFAULT '',   pun_merge_num varchar(100) DEFAULT '',   exemption_type varchar(100) DEFAULT '',   code varchar(100) DEFAULT '',   exemption_percentage varchar(100) DEFAULT '',   PRIMARY KEY (_id),   KEY date_updated (date_updated),   KEY pun_county_num (pun_county_num),   KEY pun_lease_num (pun_lease_num),   KEY pun_merge_num (pun_merge_num),   KEY exemption_type (exemption_type),   KEY code (code),   KEY exemption_percentage (exemption_percentage) ) ENGINE=InnoDB DEFAULT CHARSET=latin1;  LOAD DATA LOCAL INFILE 'test2.dat'  INTO TABLE exp_gpexempt (@_row) SET pun_county_num = TRIM(SUBSTR(@_row,1,3)), pun_lease_num = TRIM(SUBSTR(@_row,4,6)), pun_sub_num = TRIM(SUBSTR(@_row,10,1)), pun_merge_num = TRIM(SUBSTR(@_row,11,4)), exemption_type = TRIM(SUBSTR(@_row,15,50)), code = TRIM(SUBSTR(@_row,65,5)), exemption_percentage = TRIM(SUBSTR(@_row,70,24)); 

Here is the content of the test2.dat file:

00300063900000School District                                   05   00000000000.000293000000 00300365500000State School Land Commission                      01   00000000000.125000000000 00301843300000State School Land Commission                      01   00000000000.125000000000 00302942700633State School Land Commission                      01   00000000000.125000000000 00302942800633State School Land Commission                      01   00000000000.125000000000 00303004100000Federal                                           02   00000000000.067632900000 00303004200000Federal                                           02   00000000000.125000000000 00303004600000Federal                                           02   00000000000.125000000000 00303004700000Federal                                           02   00000000000.125000000000 00303004800000Federal                                           02   00000000000.125000000000  

## finding amount of errors that can be fixed based on code length [closed]

i tried to look online and search this site and others but haven’t found any good explanation to the following simple question: how many errors can a code with length k(k>2)fix?

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## Knapsack with a fixed number of weights

Consider a special case of the knapsack problem in which all weights are integers, and the number of different weights is fixed. For example, the weight of every item is either 1k or 2k or 4k. There is one unit of each item.

The problem can be solved using dynamic programming. Suppose the knapsack capacity is $$C$$, and the most valuable item of weight $$w$$ has a value of $$v_w$$. Then, the maximum value of KNAPSACK($$C$$) is the maximum of the following three values:

KNAPSACK($$v_1$$,$$C-1$$), KNAPSACK($$v_2$$,$$C-2$$), KNAPSACK($$v_4$$,$$C-4$$).

Is there a more efficient algorithm? Particularly, is there a greedy algorithm for this problem?

I tried two greedy algorithms, but they fail already for weights 1 and 2. For example, suppose there are 3 items, with values 100, 99, 51 and weights 2, 1, 1:

• If the capacity is 2, then the greedy algorithm that selects items by their value fails (it selects the 100 while the maximum is 99+51).
• If the capacity is 3, then the greedy algorithm that selects items by their value/weight ratio fails (it selects the 99+51 while the maximum is 100+99).

However, this does not rule out the possibility that another greedy algorithm (sorting by some other criterion) can work. Is there a greedy algorithm for this problem? Alternatively, is there a proof that such an algorithm does not exist?

## How i can perform most damage and mobility within this fixed classes?

My character is Air Genasi (+2 dex, -2 cha)

Classes: Fighter 2/Shadowcaster 1/Scout 1/Ardent 1;

He have next stats: STR 10 DEX 20 CON 14 INT 14 WIS 11 CHA 9

Feats: Point Blank Shot(PHB), Willing Deformity, Willing Deformity(Teeth), Weapon Finnesse

He nibbled off his hand, so he is totally one-handed and use rapier now, and off-hand 1d4 bite attack from willing deformity.

As shadowcaster (ToM book) he have a next spells: -arrow of dusk (2d4 nontlethal ray) -caul of shadow (+1 to AC deflection bonus) -steel shadows (+6 to AC)

Class was taken mostly for flavor in case of characters extraplanar heritage.

As ardent (CP book) he have next options: mantles: Freedom, Pain and Suffering; and power Dimension Hop which allows to 10 ft. move as swift action. +5 ft. for investing power points

As scout (CA book) he have a Skirmish ability (+1d6 to damage of all attacks during the round where character was moving at least 10 ft… +2d6 at 5-th lvl and so on, scalable damage)

Basic style is – 1. Dimension hop to enemy, and it triggers skirmish (because to trigger you must move, dimension hop description says that you instantly move, not teleproting, transfering or other) 2. Full attack with rapier and bite (1d6+1d6, 1d4+1d6) with +7(rap)/+2(bite) attack modifiers.

+5 dexterity bonus, and Steel Shadows help me to keep high AC. Also my character good at intimidation, stealth move and hiding. Potentially i can reach hustle (from Freedom mantle) and Flicker (from Shadowcaster class), to keep me mobile

I’m also thinking about Arcane Strike feat, but not sure.

So, questions is – what i can do, to improve basic style? Maybe there is can be some another combos, much devastating? In what class from the Ardent\Scout\Shadowcaster triad is better to progress first? second?

Books of D&D 3.5:

Player’s Handbook (PHB) Tome of Magic (ToM) Complete Adventurer (CA) Complete Psionic (CP) Expanded Psionic (EP)

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