OpenLLM-France/wikimedia huggingface dataset:
# A-level Computing/AQA/Paper 1/Fundamentals of data structures/Trees

Connected means that every node is connected to at least one other node. Undirected means there is no direction associated with an edge, i.e. lines are used, not arrows. A cycle is a circuit (a succession of edges that start and end at the same vertex) in which all the edges are different and all the vertices visited are different (apart from the start and end vertex).
A rooted tree is a tree in which one vertex has been designed as the root and every edge is directed away from the root.
* Exercise: Unordered Binary Trees
* For the following tree note the root, leaves and the left sub tree
* Answer:
* Root = 5
* Left subtree = 2, 1, 4, 3
* Leafs = 1, 3, 7, 9
* Exercise: Ordered Binary Trees
* To work out the following you begin at the root of the tree, if the second input is higher than the root it goes to the right of the root, whereas if it is lower than the root it goes to the left. the third input is then used, if it is higher than the root then it gets passed to the right, if there is already a input on this segment of the tree the input is compared with the input that is in there, if it is higher than the input it is passed to the right and if it is lower it is passed to the left, this process continues until all inputs have been dealt with and the tree is complete.
* Create a binary tree for the following data input:
* 5, 2, 6, 8, 4, 1, 9, 7, 3
* Answer:
* Create a binary tree for the following major city input:
* Monaco, Paris, Vatican, Rome, Norwich, Lewisham, New York, Partington
* Answer:
* Create a binary tree for the following list of animals:
* Elephant, Cat, Dog, Hippo, Giraffe, Lion, Bear
* Answer:
# A-level Computing/AQA/Paper 1/Fundamentals of data structures/Vectors

A vector, in computing, is generally a one-dimensional array, typically storing numbers. Vectors typically have fixed sizes, unlike lists and queues.
The vector data structure can be used to represent the mathematical vector used in linear algebra. See related pages for mathematical vector operations. Vectors are often used in computing in computer graphics and simulating physical systems.
Vectors are also used in natural language processing in computing, as a compact way to represent documents as counts of occurrences of words. For instance, the two sentences "It was the best of times, it was the worst of times" and "It was the age of wisdom, it was the age of foolishness" could be represented as two vectors:
| | "It was the best…" | "It was the age…" |
| age | 0 | 2 |
| best | 1 | 0 |
| foolishness | 0 | 1 |
| it | 2 | 2 |
| of | 2 | 2 |
| the | 2 | 2 |
| times | 2 | 0 |
| was | 2 | 2 |
| wisdom | 0 | 1 |
| worst | 1 | 0 |

### Key Formulas you should know

There are several formulas that you may be asked to use in the exam. Below they are listed along with a brief description.
Adding and subtracting values:
This is done fairly simply by adding or subtracting each element to the corresponding one in the other vector. (x, y) + (x, y) = (2x, 2y)
Convex combination of two vectors
This is expressed in the form αυ+β where α+Β=1.
For example, with the vectors (5, 3) and (4, 2) the convex of the two would be 0.7*(5, 3) +0.3*(4, 2) = (4.7, 2.7)
Dot Product of two vectors
This is simply when each component of each vector is multiplied by the corresponding component.
For example, u•v = x1*x2 + y1*y2
Finding the angle between two vectors
cosθ = (u•v) / (||u|| •||v||)
# A-level Computing/AQA/Paper 1/Fundamentals of data structures/Stacks

A stack is an ADT that might involve a dynamic or static implementation. A stack is a last-in-first-out (LIFO) or first-in-last-out (FILO) ADT. Implementations should include two operations, pushing and popping, and a pointer to the top of the stack.
A real life example is a stack of books you might have on your desk:
Let's take a look at a computer implementation of a stack:
* Pushing: Adds a new specified item to the top of the stack
* Popping: Removes the item from the top of the stack.
| State 1 | State 2 | State 3 | State 4 | State 5 |
| Push 'elephant' | Push 'hippo' | Push 'zebra' | Pop | Push 'flamingo' |
| memlocdataTopOfStack 4 3 2 1elephant<-- | memlocdataTopOfStack 4 3 2hippo<-- 1elephant | memlocdataTopOfStack 4 3zebra<-- 2hippo 1elephant | memlocdataTopOfStack 4 3zebra 2hippo<-- 1elephant Note the data isn't 'deleted' The TopOfStack pointer moves to show it is no longer in the stack | memlocdataTopOfStack 4 3flamingo<-- 2hippo 1elephant |
Stacks have several uses:
* Reversing queues (as seen above with the Alphabetised names)
* Performing Reverse Polish Calculations (see ....)
* Holding return addresses and system states for recursive function calls
Exercise: Stacks
Draw the stack after each of the following commands, starting with an empty stack. What does the stack achieve:
Push 'Annabelle'
Push 'Chris'
Push 'Hemingway'
Push 'James'
Pop
Pop
Pop
Pop
Answer:
Command 1Command 2Command 3Command 4
memlocdataTopOfStack
4
3
2
1Annabelle<--
memlocdataTopOfStack
4
3
2Chris<--
1Annabelle
memlocdataTopOfStack
4
3Hemingway<--
2Chris
1Annabelle
memlocdataTopOfStack
4James<--
3Hemingway
2Chris
1Annabelle
Command 5Command 6Command 7Command 8
memlocdataTopOfStack
4James
3Hemingway<--
2Chris
1Annabelle
Output: James
memlocdataTopOfStack
4James
3Hemingway
2Chris<--
1Annabelle
Output: Hemingway
memlocdataTopOfStack
4James
3Hemingway
2Chris
1Annabelle<--
Output: Chris
memlocdataTopOfStack
4James
3Hemingway
2Chris
1Annabelle
Output: Annabelle
Top of Stack = 0
The stack is empty
This set of instructions used the stack to input data in order and then output it in reverse order
Give the set of instructions required to get from State 1 to State 2 as shown below:
State 1State 2
memlocdataTopOfStack
4
3Sharks<--
2Chalk
1Cheese
memlocdataTopOfStack
4
3Witches<--
2Sand
1Cheese
Answer:
Pop
Pop
Push 'Sand'
Push 'Witches'
If we have an empty Stack what do we set the pointer TopOfStack to?
Answer:
0 or null
Describe the Stack data type:
Answer:
A stack is a First In Last Out or Last In First Out data type
Give two uses for a Stack in a computer:
Answer:
Reversing queues (as seen above with the Alphabetised names)
Performing Reverse Polish Calculations (see ....)
Holding return addresses of recursive function calls :
# A-level Computing/AQA/Paper 1/Fundamentals of databases/Normalisation

It is a way of reducing data redundancy and inconsistency...

## See also

* w:Database_normalization
# A-level Economics/OCR/2884
## Economics Of Work And Leisure Module 2884

This module is concerned with labour from the viewpoint of both the individual and industry. As well as focusing later in the module on the leisure industry and several specific markets eg.(Air Travel, Spectator sports etc.). It is best to be aware that this particular module is trying to make students ever aware of the trade-off between Leisure and Work, understanding this trade off fully will provide students with sufficient knowledge to cover many parts of the syllabus easily.
# A-level Economics/OCR/Introduction to economics-Whats the problem

What is the problem?
Economics is the study of how to allocate or use resources such as money, land, etc. most efficiently. The world is such that everything is scarce. Money is limited, food is limited, labor is limited, steel and plastic are limited. Everything is limited and thus to do something we need to make sure that resources are allocated in the best and the most efficient way.
Opportunity cost?
One problem here is that of opportunity cost. It is the "next best alternative that has been forgone" while undertaking something. An example is that a person eats ice cream, the next best alternative was eating a burger, which was not undertaken, thus the cost of eating an ice cream is eating burger. This cost exists because the person has a limited amount of money and only one thing can be bought. Companies and governments have to look at opportunity costs as well as time and money when making decisions.
Scare resources?? What are the scarce resources then?? In economics they are:
* Entrepreneur (defined in economics as anyone who takes a risk)
* Land (your land on which you built a plant, office or mine etc.)
* Labour (employees, skilled and unskilled labour)
* Capital (this includes money, machinery etc.)
Increasingly another factor is added i.e.
# A-level English/The Miller's Prologue and Tale

A-level Study Guide - 'The Miller's Prologue and Tale'
* Past Paper Questions
* Notes on the Miller's Tale
* Characters
* Themes
* Contrast with 'The Knight's Tale
# A-level Economics/OCR/2881

Module 2881 The Market System
This module provides an introduction as to why economic choices have to be made and how the market model operates. The subject content covers the basic principles of:
* why individuals, organisations and societies have to make choices;
* how competitive markets work;
* the objectives and competitive behaviour of firms and how explanations of market structure are used by economists to explain this behaviour.

## Managing Scarce Resources

The main economic problem is scarce resources in relation to infinite wants. Everybody must make choices, in economics this is known as opporunity cost. Opportunity Cost: In decision making the next best alternative that could have been chosen. The opportunity cost thus leads to an important tool in economics that is Marginal analysis. Marginal analysis: An approach to economic decision making based on considering the additional(marginal) benefits and costs of a small change in behavior.
# A-level Economics/OCR

This WikiBook will attempt to create a useful revision resource/textbook for those people undertaking the OCR A-Level Economics qualification.

## Modules

Introduction to economics-Whats the problem
Module 2881: The Market System Module 2882: Market Failure & Government Intervention Module 2883: The National And International Economy Module 2884: Economics of Work and Leisure Module 2885: Transport Economics
# Analysis and Design of the Traffic Control System

* Introduction
* Users
* Detectors
* Controllers
* Displays
# Analogue Electronics/Operational Amplifiers

An operational amplifier ("op-amp") is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. An op-amp produces an output voltage that is typically hundreds or thousands of times larger than the voltage difference between its input terminals.
Operational amplifiers had their origins in analog computers where they were used to do mathematical operations in many linear, non-linear and frequency-dependent circuits.
Characteristics of a circuit using an op-amp are set by external components with little dependence on temperature changes or manufacturing variations in the op-amp itself, which makes op-amps popular building blocks for circuit design.
# Analytic Combinatorics
## Introduction

Analytic Combinatorics uses techniques from complex analysis to find estimates for the coefficients of generating functions.
It relates the discrete world of enumerative combinatorics to the continuous world of complex analysis.
It is associated with the work of Philippe Flajolet and Robert Sedgewick, although its techniques can be traced back to at least the early 20th century to people like Srinivasa Ramanujan and G. H. Hardy.

## Prerequisites

This book assumes you already have a reasonable understanding of generating functions.
It assumes little to no understanding of complex analysis. It should explain any complex analysis that you need to know.
The individual chapters will list their own prerequisites.

## Chapters

* Cauchy-Hadamard theorem and Cauchy's inequality
* Meromorphic Functions
* Darboux Method
* Tauberian Theorem
* Singularity Analysis
* Saddle-point Method
# Analogue Electronics/BJTs/Active Mode/ß dimensional Analysis

This page will show that β, the common-emitter current gain of a BJT has no units.
β is given by:
       $\beta =1/\left({{\frac {D_{p}N_{A}W}{D_{n}N_{D}L_{p}}}+{\frac {1}{2}}{\frac {W^{2}}{D_{n}\tau _{b}}}}\right)$
where
* D$_p$ and D$_n$ are the hole and electron diffusivity, in cm$^2$ s$^{−1}$
* N$_D$ and N$_A$ are the donor and acceptor doping concentrations, in cm$^{−3}$
* W is the base width, in cm
* L$_p$ is the hole diffusion length in the emitter, in cm
* τ$_b$ is the minority carrier lifetime in the base, in s
So we have:
       $\left[\beta \right]=\left({{\frac {L^{2}T^{-1}L^{-3}L}{L^{2}T^{-1}L^{-3}L}}+{\frac {L^{2}W^{2}}{L^{2}T^{-1}T}}}\right)^{-1}$
Notice that the first term in the addition is a ratio of two quantities with identical dimensions. This leaves us with:
       $\left[\beta \right]=\left({\frac {L^{2}}{L^{2}T^{-1}T}}\right)^{-1}=\left({\frac {L^{2}}{L^{2}}}\right)^{-1}$
We now have the reciprocal of a ratio of identically dimensioned quantities. Therefore, β is dimensionless.
# Analogue Electronics/Instrumentation Amplifiers

Amplifiers are electronic devices or equipments which used to increase the strength of audio or video signals.
# Analogue Electronics/Current Mirrors

The Wilson Current Mirror is a simple method to make a very accurate current mirror with a very high output resistance, meaning little deviation in the current delivered.
# Analogue Electronics/BJTs/Active Mode/Band Diagrams
## Band Diagrams

We can consider the action of an NPN BJT using band diagrams. With no applied voltages, we see the following shape:
Clearly, no current can flow, as the "hump" in the middle stops current in both directions. Now, if we apply voltages as we did above we get the following result:
The EBJ potential barrier lowers, and some electrons can drift across into the base, whereupon they are swept up by the electric field from the collector, and "fall" down the potential hill into the collector. A few holes also diffuse from base to emitter.
# Ada Programming/Attributes/'Pool Address
## Description

X'Pool_Address for any object X returns the address of X within its storage pool. This is the same as X'Address, except that for an unconstrained array whose bounds are allocated just before the first component, X'Pool_Address returns the address of those bounds, whereas X'Address returns the address of the first component.
Here, we are interpreting ‘storage pool’ broadly to mean wherever the object is allocated, which could be a user-defined storage pool, the global heap, on the stack, or in a static memory area. For an object created by new, Ptr.all'Pool_Address is what is passed to Allocate and returned from Deallocate.
# Ada Programming/Attributes/'Position
## Description

'Position is a record type component attribute. It represents the address offset of the component from the beginning of the record. The value returned is represented in storage units, which is machine-specific. The attribute is closely related to the attributes 'First_Bit and 'Last_Bit. Together they specify the Layout aspect of records.
See Representation Clauses.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Attributes
* Ada Programming/Attributes/'Bit_Order

### Ada Reference Manual

* 13.3: Operational and Representation Attributes
* Annex K: Language-Defined Attributes
# Ada Programming/Attributes/'Output
## Description

Writes the value of X to Stream, including any bounds or discriminants.
# Ada Programming/Attributes/'Parallel Reduce
## Description

Reduction expression that yields a result equivalent to replacing the attribute identifier with Reduce and the prefix of the attribute with the value_sequence.
X'Parallel_Reduce is a reduction expression that yields a result equivalent to replacing the attribute identifier with Reduce and the prefix of the attribute with the value_sequence:
[parallel for Item of X => Item]
# Ada Programming/Attributes/'Passed By Reference
## Description

typ'Passed_By_Reference for any subtype returns a value of type Boolean value that is True if the type is normally passed by reference and False if the type is normally passed by copy in calls. For scalar types, the result is always False and is static. For non-scalar types, the result is nonstatic.
# Ada Programming/Attributes/'Pos
## Description

The 'Pos attribute is defined for all discrete types. It is a function returning the argument's position number as a universal_integer; the prefix S must be a subtype name. (Universal integers are implicitly converted to any specific integer type as required by the context.)
For enumeration types, position numbers start at 0; if the argument does not denote a valid value (perhaps because of an uninitialized variable), the exception Program_Error is raised. For integer types, the attribute returns the value converted to universal_integer. Note that it is not necessary for the actual argument to belong to the subtype S.
Note that representation clauses do not affect position numbering. Whatever underlying value the enumerated value has, the position number will remain the same.

## Example

Another example without representation clause:

## See also

The inverse of the 'Pos attribute is 'Val.
The underlying representation can be obtained using an Unchecked_Conversion, or with the implementation-defined attribute 'Enum_Rep (GNAT).
For a detailed explanation of universal_integer, see Type System: Elaborated Discussion of Types for Signed Integer Types.

### Wikibook

* Ada Programming
* Ada Programming/Attributes/'Val
* Ada Programming/Attributes/'Valid

### Ada Reference Manual

* 13.3 Operational and Representation Attributes (Annotated)
* Annex K Language-Defined Attributes (Annotated)
# Ada Programming/Attributes/'Object Size
## Description

The size of an object is not necessarily the same as the size of the type of an object. This is because by default object sizes are increased to be a multiple of the alignment of the object. For example, Natural'Size is 31, but by default objects of type Natural will have a size of 32 bits. Similarly, a record containing an integer and a character:
will have a size of 40 (that is Rec'Size will be 40). The alignment will be 4, because of the integer field, and so the default size of record objects for this type will be 64 (8 bytes).
If the alignment of the above record is specified to be 1, then the object size will be 40 (5 bytes). This is true by default, and also an object size of 40 can be explicitly specified in this case.
A consequence of this capability is that different object sizes can be given to subtypes that would otherwise be considered in Ada to be statically matching. But it makes no sense to consider such subtypes as statically matching. Consequently, GNAT adds a rule to the static matching rules that requires object sizes to match. Consider this example:
In the absence of lines 5 and 6, types R1 and R2 statically match and hence the conversion on line 12 is legal. But since lines 5 and 6 cause the object sizes to differ, GNAT considers that types R1 and R2 are not statically matching, and line 12 generates the diagnostic shown above.
Similar additional checks are performed in other contexts requiring statically matching subtypes.
# Ada Programming/Attributes/'Old
## Description

The value of X on entry, has same type as X.
Each X'Old in a postcondition expression that is enabled, other than those that occur in subexpressions that are determined to be unevaluated, denotes a constant that is implicitly declared at the beginning of the subprogram body, entry body, or accept statement.
# Ada Programming/Attributes/'Overlaps Storage
## Description

Returns True if the representation of X2 shares at least one bit with the representation of the object denoted by X.
The actual parameter shall be a name that denotes an object. The object denoted by the actual parameter can be of any type. This function evaluates the names of the objects involved and returns True if the representation of the object denoted by the actual parameter shares at least one bit with the representation of the object denoted by X; otherwise, it returns False.
# Ada Programming/Attributes/'Partition ID
## Description

Identifies the partition in which D was elaborated.
Denotes a value of the type universal_integer that identifies the partition in which D was elaborated. If D denotes the declaration of a remote call interface library unit the given partition is the one where the body of D was elaborated.
# Beekeeping/Mead Making

There already exists a free Wiki Cookbook for information about mead. Wiki Cookbook Mead Page
# Beekeeping/Pheromones
## How do honey bees use pheromones to communicate?

Bees use chemical cues to interact with each other and to manage colony organization. Alarm pheromone is used to recruit bees to defend the colony, while Nasanov pheromone is used for aggregation (during swarming or if bees are displaced from the colony).The forager bees produce a pheromone which slows the behavioral maturation of young bees so that they remain in the nursing state longer – this allows the colony to adjust the worker force to have the optimal number of nurses and foragers. The virgin queen releases a pheromone which is used to signal to drones during mating. After mating, the chemical composition of this pheromone changes, and it will inhibit the rearing of new queens, slow behavioral maturation of workers, and inhibit the development of ovaries in workers (so they remain sterile). Queen pheromone also attracts workers from a short distance, and causes them to lick and antennate the queen in a “retinue response”. The workers in the retinue thus pick up the pheromone and spread it throughout the colony. The developing larvae produce brood pheromone, which stimulates feeding of the larvae, capping of the cells prior to pupation, and also slows the behavioral maturation of workers and inhibits worker ovary development. Exposure to both brood and queen pheromone will stimulate foraging behavior in forager bees.
# Beekeeping/Plants for Bumblebees

Bumblebees have a rather long tongue; shorter than those butterflies like atalantas but longer than those of honey bees. As such, they prefer flowers such as:
* Cynara scolymus
* Monarda
* Centaurea montana, Centaurea scabiosa, Centaurea nigra
* Digitalis purpurea
* Salvia spp
* Agastache foeniculum
* Lotus corniculatus
* Achillea millefolium
* Solidago
* Lonicera periclymenum
* Lobelia cardinalis
* Origanum
* Trifolium
* Tropaeolum majus
* Pulmonaria saccharata
* Marrubium vulgare
* Phacelia tanecetifolia
* Leucanthemum x superbum
* Centranthus ruber
* Echium vulgare

## References

* ↑ HDRA encyclopedia of organic gardening by Pauline Spears

## Note

It should be noted that the list of plants mentioned above may or may not be native to your area. As such, if you wish to use them, check whether they are native to your area first.
# Beekeeping/Plants for Honey Bees

Honey bees have a rather short tongue; shorter than those of bumblebees and butterflies like atalantas. As such, they prefer flowers such as:
* Nemesia
* Melissa officinalis
* Mahonia
* Viburnum
* Borago officinalis
* Rubus spp
* Erica
* Rosa canina
* Reseda odorata
* Erysimum
* Pastinaca sativa
* Perovskia atriplicifolia
* Rosmarinus officinalis
* Iberis
* Arabis
* Verbascum
* Vicia faba
* Parthenocissus quinquefolia
* Isatis tinctoria
* Chamerion angustifolium
* Verbena officinalis
* Daucus carota

## Note

It should be noted that the list of plants mentioned above may or may not be native to your area. As such, if you wish to use them, check whether they are native to your area first.

## References

* ↑ HDRA encyclopedia of organic gardening by Pauline Spears