OpenLLM-France/wikimedia huggingface dataset:
# Introductory Agrometeorology/Earth Atmosphere
## Atmosphere

Atmosphere
** colourless, odourless and tasteless physical mixture of gasses.
** surrounds earth on all sides.
** mobile, compressible and expandable.
** contains huge number of solid and liquid particles called aerosol.
The lower atmosphere where the chemical composition of gas is uniform is called homosphere. At higher levels the chemical composition of air changes considerably and known as heterosphere.
Atmosphere
* Provides oxygen which is useful for crop respiration
* Provides CO2 to build biomass in photosynthesis.
* Provides N, which is essential for plant growth.
* Acts as a medium for transportation of pollen.
* Protects crops and human beings from harmful UV rays.
* Provides rain to field crops.

## Composition of atmosphere

The following all the different gases that are present in percentage by volume approximately.
a. gases
* Nitrogen (N2) = 78.08
* Oxygen (O2) = 20.95
* Argon (Ar) =0.93 CO2 =0.03
* Neon (Ne) = 0.0018 Helium(He) =0.0005
* Ozone(O3) =0.00004 Hydrogen(H2) =0.00006
* Methane (CH4) =0.00017
b. water vapour: 0.02% by volume in a cold dry climate to nearly 4% in the humid tropics.
c. dust particles:

## Structure

* Troposphere:Gr.‘tropos’=“mixing”/turbulence
** avg. height is 14 km above sea level (poles is about 8 km, equator is about 16 km)
** shallow layer separating troposphere from the next thermal layer of the atmosphere (stratosphere) is tropopause. Various clouds, thunderstorms, cyclones and anticyclones occur in this sphere because of the concentration of almost all the water vapour (4% of the atmosphere composition) aerosols in it.
** decrease in temperature with increasing elevation up to 14 km.
* Stratosphere: (16-30 km)
** no visible weather phenomena occur above tropopause.
** gradual temperature increase with height beyond 29 km.
* Ozonosphere (or Mesosphere):
** maximum concentration of ozone between 30 and 69 km above the surface of the earth
** temperature increases with height @ 5oC/km.
* Ionosphere:60 km above the earth’s surface
** temperature falls again reaching a minimum of about 100oC at a height of 80 km above earth’s surface. Beyond this level, the temperature increases again
* Exosphere: 400 and 1000 km
** density of atoms in the atmosphere is extremely low.
** Hydrogen and helium gases predominate in the outer most region

## Lapse Rate

The decrease in air temperature with height is known as the normal/environmental lapse rate and it is 6.5°C/km.
← Introduction · Solar radiation →
# Introductory Agrometeorology/Micro-climate Modification
## Micro climatic modification

- Artificial control of field environment to keep the optimum condition of plant growth and crop production - A practice of environmental control requires a complete knowledge of physiology of plants and physical environment.
it is be done through:
* Controlling wind velocity
* Controlling heat load
* Controlling water balance.
← Agrometeorological Normals for Crops · Agroclimatic Regionalization →
# HydroGeoSphere/IBM Data Explorer (OPENDX)

The following instructions can be used to export data generated by grok to IBM Data Explorer (OPENDX).

## Mesh to opendx

* odxfile Name of the file to which the 3-D mesh information (blocks or prisms) will be written in OPENDX readable format.

## Wells to opendx

* odx_wells_file Name of the file to which the 1-D well element information will be written in OPENDX format.
* odxfile Name of the file which contains the 3-D mesh information, as given in the Mesh to opendx instruction.

## Tiles to opendx

* odx_tiles_file Name of the file to which the 1-D tile element information will be written in OPENDX format.
* odxfile Name of the file which contains the 3-D mesh information, as given in the Mesh to opendx instruction.
# HydroGeoSphere/Imported from FRACTRAN
## Fractran properties

This instruction is to be used after a mesh has been loaded using the Read fractran 2d grid instruction described in Section 5.3.5.1. It uses the FRACTRAN prefix defined there to read the associated properties.
# HydroGeoSphere/Initial Conditions

* Subsurface Flow
* Surface Flow
* Transport
** Solute Definition
** Travel Time Probability
** Heat Transfer
# HydroGeoSphere/Interactive 3-D Mesh Generator

Irregular grids can be generated by supplying nodal coordinates, element incidences and element zones for a 2-D slice which is composed of triangular or quadrilateral elements. Currently, triangles and quadrilaterals can not be mixed in the same slice. These slices can then be replicated to form a 3-D mesh composed of 6-node prisms (from triangles) or 8-node hexahedra (from quadrilaterals).
# HydroGeoSphere/Interactive Block Grids

Interactive block instructions can be used to generate a grid made up of variably-sized blocks. The user can grade the mesh as desired in each of the 3 principal directions. This is particularly useful for regions in which fine meshes are required, for example, near a discrete fracture or well.
Note that these instructions cannot be used in conjunction with the other grid generation instructions like Generate uniform/variable blocks/prisms.

## Generate blocks interactive...End

Causes grok to begin reading a group of interactive block instructions until it encounters an End instruction. The group should contain of at least one instruction for each of the principal directions.
The available instructions are:

## Grade x

* x1, x2, dxstart, xfac, dxmax Start and end x-coordinate, starting element size,
element size multiplication factor and maximum element size.
Grid lines (i.e. elements) are generated along the x-axis from x1 to x2 which grade up in size from dxstart to dxmax. Element sizes are increased steadily by a factor of xfac.

## Grade y

As above but for the y-axis.

## Grade z

As above but for the z-axis.

## Example block grid

The instructions used to generate the mesh shown in Figure 5.2 are:
# HydroGeoSphere/Hydromechanical Stress

Hydromechanical stresses can be computed externally and used as input to grok using the following instruction:

## Elemental stress field from files

* npanel Number of panels (i.e. files) defining the time-variable external stress field. For each panel, enter the following:
       (a) ton_val, esvfile Time on [T] and name of file containing elemental stress stress values [L].
This information is passed to HydroGeoSphere. At each timestep, the current time is compared to the array ton_val to determine whether or not to apply the update the current set of elemental stress values by reading the next file in the list.
Each file must be in ASCII format and contain a list of elemental stress values (i.e. one value for each element in the 3-D domain), expressed as equivalent freshwater head.
# HydroGeoSphere/Inactive Elements

These instructions can be used to discretize irregular boundaries with block elements by deactivating portions of the grid, where all elements become inactive for both the flow and transport simulation. Elemental assembly is skipped and all nodes that only belong to the inactive element, and are not at all connected to active elements, are assigned default values of head and concentration equal to -9999.0. This option is similar to what is done in MODFLOW to specify inactive cells.

## The elements becomes inactive

All chosen elements will become inactive.

## Make zone inactive

All elements in the current set of chosen zones will become inactive.
For a 2-D slice made of 4-node rectangular elements, the following instruction can be used to make elements inactive:

## Make element inactive using shapefile

* arcview_prefix Prefix of the ARCVIEW shape file.
* unproject_file If .TRUE, this logical switch causes grok to read grid unprojection data as described in Section 5.3.10 and to apply it to the data read from the ARCVIEW shapefile.
* project_file If .TRUE, this logical switch causes grok to read grid projection data as described in Section 5.3.10 and to apply it to the data read from the ARCVIEW shapefile.
* outside If .TRUE, elements located outside the area defined in the ARCVIEW shapefile will become inactive. If .FALSE, elements located inside the area will become inactive.

## Write inactive elements to file

* inactive_file Name of the file to which the inactive element information will be written.
Setting up inactive elements with the Make element inactive using shapefile instruction can be time consuming in grok and this step does not need to be repeated as long as the grid structure remains the same. This instruction is intended to be used in conjunction with the following instruction.

## Read inactive elements from file

* inactive_file Name of the file from which the inactive element information will be read.
The results of successive calls to this instruction are cumulative, if different sets of inactive elements are read.
# HydroGeoSphere/Heat Transfer Properties

To enable heat transfer, you must define the temperature species in the solute definition block as described in Section 5.6.3.1. Note that the unit for temperature must be °C and that all heat transfer properties must be given in the SI-units kilogram-meter-second Celsius. The thermal properties of the solids are specified in the material property file. The following instructions can be used to control the heat transfer solution:
The available instructions are:

## Thermal conductivity of water

* k_l [W L$^{−1}$ K$^{−1}$] Thermal conductivity of the liquid phase.
Assigns a uniform value to the thermal conductivity of groundwater. If this instructions is used, the thermal conductivity of water is assumed constant and equal to $k_{l}$. It is therefore not calculated from the water temperature, which is the default setting.

## Specific heat capacity of water

* c_l [J kg$^{−1}$ K$^{−1}$] Specific heat capacity of the liquid phase.
Assigns a uniform value to the specific heat capacity of water. If this instructions is used, the specific heat capacity of water is assumed constant and equal to $c_{l}$. It is therefore not calculated from the water temperature, which is the default setting.

## Mechanical heat dispersion

Causes mechanical heat dispersion to be simulated. The default is no mechanical heat dispersion.
The following instruction can be used to define initial temperatures for the problem:

## Initial temperature profile

* temp_top [°C] The temperature at the top of the domain.
* temp_grad [K m$^{−1}$] The prevailing geothermal gradient.
Calculates a depth profile of temperature and assigns the values to the initial temperature.
The following instructions can be used to define the heat source boundary condition:

## Zero order source

* npanel Number of panels in the time-variable, zero-order source function. For each panel, enter the following:
          (a) ton_val,toff_val, (bc_val(j),j=1,nspeciesmob) Time on [T], time off [T] and mass of solute produced per unit volume of porous medium solids per unit time
             [M L$^{−3}$].
Nodes in the chosen zones area assigned zero-order source boundary conditions.
A panel is a point in time at which the source term is set to a new value. The first panel would normally start at time zero. The source term given for the last panel will be maintained until the end of the simulation. You can assign a static source term for the duration of the simulation by setting npanel to 1, ton_val to 0.0 and toff_val to a large number.
Note that if nspeciesmob is greater than 1, additional values of bc_val should be included.

## Exponential zero order source

* heat_q_zero Heat production at t = 0.
* heat_constant Constant in the exponential function.
Nodes in the chosen zones area assigned an exponentially decreasing zero-order heat source boundary conditions.
# HydroGeoSphere/Immiscible Phase Dissolution Source

An immiscible phase dissolution source is one in which it is assumed that there is dissolution of an immobile liquid or solid phase into the subsurface water until all dissolvable material is exhausted. The following instruction can be used to define the source:

## Immiscible phase dissolution data

* diss_mass Mass of dissolvable material per unit volume of porous medium.
* diss_conc The aqueous solubility value for the immiscible phase in mass of solute per unit volume of aqueous solution.
Chosen nodes are assigned first-type concentration values equal to diss_conc, which are maintained until all the material associated with a node is dissolved, at which time the node reverts back to an unconstrained condition. Once unconstrained, any water flowing in will generate mass due to the nonzero concentration, and so dissolution nodes should not be located on the outer surface of the domain.
It is assumed that the total mass of dissolvable material is located in the matrix only. The total mass available for dissolution associated with a given node is then calculated by multiplying contributing volume (from all shared elements) times the porosity times the variable diss_mass.
# HydroGeoSphere/Imported from GMS
## Read gms transport boundary conditions

* gmsfile Name of the file which contains the GMS boundary condition data.
Reads a GMS boundary condition file which has been produced by the FEMWATER module and extracts pertinent transport boundary condition information.
Currently, only Dirichlet and Cauchy transport boundary conditions are recognized by HydroGeoSphere. Also, this feature only works for a single species. If more than one species is present in the simulation, use the instructions specified concentration and specified third-type concentration to define the input data.
Dirichlet (first-type) boundary conditions can be assigned in GMS using the Select Boundary Nodes tool in the 3D mesh module. Once the appropriate nodes are chosen, you can assign the boundary condition using the Assign Node/Face BC... tool under the FEMWATER menu option. In the GMS Node BC dialog, you can select either Constant or Variable concentration to produce a static or time-variable concentration function.
Cauchy (third-type) boundary conditions can be assigned in GMS using the Select Boundary Faces tool in the 3D mesh module. Once the appropriate faces are chosen, you can assign the boundary condition using the Assign Node/Face BC... tool under the FEMWATER menu option. In the GMS Node BC dialog, you should select Flux then Constant or Variable to produce a static or time-variable mass flux function.
# Irish/The Article

Lessons
Unit One: 1 2 3 4
Unit Two: 1 2 3 4 5 6
Unit Three: Lesson Index
Language Reference
Spelling and Pronunciation - Grammar
Wikiversity
More Irish language resources can be found at Wikiversity's Department of Irish Studies

## The Article

English has a definite article ("the") and an indefinite article ("a" or "an").
Irish has only a definite article. In situations where "a" or "an" would be used in English, the noun is used with no article.
The definite article has two forms: an and na.
* an is used in front of singular nouns
* na is used in front of plural nouns (and feminine nouns in the genitive case).

## Grammatical Changes

The singular definite article "an" may change the noun it is applied to, depending on the first letter and gender of the noun:
| | Consonant (b c f g m p) | Consonant (d n t l r) | Consonant (s but not sc, sm, sp or st) | Vowel |
| Masculine | (no change) | (no change) | (no change) | t-/t |
| Feminine | séimhiú | (no change) | t | (no change) |
The plural definite article "na" changes the noun based only on its first letter:
| Consonant | Vowel |
| (no change) | "h" prefix |
# Irish/Unit 1

Lessons
Unit One: 1 2 3 4
Unit Two: 1 2 3 4 5 6
Unit Three: Lesson Index
Language Reference
Spelling and Pronunciation - Grammar
Wikiversity
More Irish language resources can be found at Wikiversity's Department of Irish Studies
Fáilte (Welcome) to Unit 1 of Wikibooks Irish!
Unit 1 provides an introduction to the Irish language for students who have little or no experience with Irish.
Unit 1 focuses on the aspects of Irish that are hardest for English speakers to learn, and most damaging to start with bad habits: spelling and pronunciation. You'll also learn the basic building blocks of the Irish sentence and how the parts of the speech fit together. Unit 1 will introduce some key Irish vocabulary, but the focus will stay on the fundamentals of pronunciation, grammar, and syntax. Remember that each language concept introduced in Unit 1 will be repeated and expanded upon in Unit 2, allowing you, the learner, to concentrate here on the sound and feel of the Irish language and perfecting your pronunciation.
One of the most important ways to learn to read and pronounce Irish is to hear it spoken and to speak it yourself. The lessons will include links to pronunciation resources outside of Wikibooks, featuring speakers from all of the major Irish dialects. Please follow these links, listen, and try repeating each word aloud.
At the end of Unit 1, we hope you will have a solid foundation in Irish spelling and pronunciation, a small but useful vocabulary of common Irish words, and an understanding of the differences between Irish and English grammar.
Tosaímis! (Let's begin!)
# Irish/Unit 2

Lessons
Unit One: 1 2 3 4
Unit Two: 1 2 3 4 5 6
Unit Three: Lesson Index
Language Reference
Spelling and Pronunciation - Grammar
Wikiversity
More Irish language resources can be found at Wikiversity's Department of Irish Studies
# LMIs in Control/Robustness

      * Continuous Time
      * Discrete Time
      * Robust H inf State Feedback Control
# LMIs in Control/Stability Analysis

      * Continuous Time
      * Discrete Time
      * Lure's Systems
      * Stability of Systems with Integral Quadratic Constraints
      * Sector Conditions
      * Kharitonov-Bernstein-Haddad
# LMIs in Control/Stability Analysis/Continuous Time/Hurwitz Stabilizability

This section studies the stabilizability properties of the control systems.

## The System

Given a state-space representation of a linear system
    ${\begin{aligned}\ \rho x=Ax+Bu\\\ y=Cx+Du\\\end{aligned}}$
Where $\rho$ represents the differential operator ( when the system is continuous-time) or one-step forward shift operator ( Discrete-Time system). $x\in \mathbb {R} ^{n},y\in \mathbb {R} ^{m},u\in \mathbb {R} ^{r}$ are the state, output and input vectors respectively.

## The Data

$A,B,C,D$ are system matrices.

## Definition

The system , or the matrix pair $(A,B)$ is Hurwitz Stabilizable if there exists a real matrix $K$ such that $(A+BK)$ is Hurwitz Stable. The condition for Hurwitz Stabilizability of a given matrix pair (A,B) is given by the PBH criterion:
    ${\begin{aligned}\ rank{\begin{bmatrix}sI-A&B\end{bmatrix}}&=n,\forall s\in \mathbb {C} ,Re(s)\geq 0\\\end{aligned}}$         (1)
The PBH criterion shows that the system is Hurwitz stabilizable if all uncontrollable modes are Hurwitz stable.

## LMI Condition

The system, or matrix pair $(A,B)$ is Hurwitz stabilizable if and only if there exists symmetric positive definite matrix $P$ and $W$ such that:
    ${\begin{aligned}AP+PA^{T}+BW+W^{T}B^{T}<0\\\end{aligned}}$         (2)
Following definition of Hurwitz Stabilizability and Lyapunov Stability theory, the PBH criterion is true if and only if , a matrix $K$ and a matrix $P>0$ satisfying:
    ${\begin{aligned}(A+BK)P+P(A+BK)^{T}<0\\\end{aligned}}$         (3)
Letting
    ${\begin{aligned}W=KP\\\end{aligned}}$         (4)
Putting (4) in (3) gives us (2).

## Implementation

This implementation requires Yalmip and Mosek.
* https://github.com/ShenoyVaradaraya/LMI--master/blob/main/Hurwitz_Stabilizability.m

## Conclusion

Compared with the second rank condition, LMI has a computational advantage while also maintaining numerical reliability.

## References

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
* LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.
* LMIs in Control Systems: Analysis, Design and Applications - by Guang-Ren Duan and Hai-Hua Yu, CRC Press, Taylor & Francis Group, 2013
# LMIs in Control/SolutionInTermsofRiccatiInequalities

Let us now come back to the H∞-problem by output feedback control. This amounts to finding the matrices $(A_{K},B_{K},C_{K},D_{K})$ such that the conditions K stabilizes P and achieves ${\bar {S}}(P,K)_{\infty }<1$. are satisfied. We proceed as in the state-feedback problem. We use the Bounded Real Lemma to rewrite the H∞ norm bound into the solvability of a Riccati inequality, and we try to eliminate the controller parameters to arrive at verifiable conditions.

## The System

Matrices to controller that solve the the H∞-problem by output feedback control
$(A_{K},B_{K},C_{K},D_{K})$

## The Data

Following matrices are needed as Inputs:.
    $(A_{K},B_{K},C_{K},D_{K})$.
    $(A,B_{1},B_{2},C_{1},C_{2})$.

## The Optimization Problem

In control systems theory, many analysis and design problems are closely related to Riccati algebraic equations or inequalities. Find X and Y

## The LMI:

There exist $A_{K},B_{K},C_{K},D_{K}$ that solve the output-feedback H∞ problem (K that stabilizes P and achieves ${\bar {S}}(P,K)_{\infty }<1$) if and only if there exist X and Y that satisfy the two ARIs
$A^{T}X+XA+XB_{1}B_{1}^{T}X+C_{1}^{T}-C_{2}^{T}C_{2}<0$
$AY+YA^{T}+YC_{1}^{T}C_{1}Y+B_{1}B_{1}^{T}-B_{2}B_{2}^{T}<0$
and the coupling condition
    ${\begin{aligned}{\displaystyle {\begin{aligned}{\begin{bmatrix}X&I\\\ I&Y\end{bmatrix}}<0\end{aligned}}}\\\end{aligned}}$

## Conclusion:

Let U and V be square and non-singular matrices with $UV^{T}=I-XY$, and set $L=-X^{-1}C_{2}^{T}$ ,$F:=-B_{2}^{T}Y^{-1}$. Then $A_{K},B_{K},C_{K}$ as defined in
$A_{k}=-U^{-1}[A^{T}+X(A+LC_{2}+B_{2}F)Y+X(B_{1}+LD_{21})B_{1}^{T}+C_{1}^{T}(C_{1}+D_{12}F)Y]V^{-T}$
$B_{K}=U^{-1}XL$
$C_{K}=FYV^{-T}$
lead to a controller K that stabilizes P and achieves ${\bar {S}}(P,K)_{\infty }<1$

## External links

* http://control.asu.edu/MAE598_frame.htm LMI Methods in Optimal and Robust Control- A course on LMIs in Control by Matthew Peet.
* https://https://arxiv.org/abs/1903.08599/ LMI Properties and Applications in Systems, Stability, and Control Theory] - A List of LMIs by Ryan Caverly and James Forbes.
* https://web.stanford.edu/~boyd/lmibook/ LMIs in Systems and Control Theory- A downloadable book on LMIs by Stephen Boyd.
# LMIs in Control/Stability Analysis/Continuous Time

      * D-Stability
      * Time-Delay Systems
      * Parametric, Norm-Bounded Uncertain System Quadratic Stability
      * Stability of Structured, Norm-Bounded Uncertainty
      * Stability under Arbitrary Switching
      * Quadratic Stability Margins
      * Stability of Linear Delayed Differential Equations
      * H infinity Norm for Affine Parametric Varying Systems
      * Entropy Bond for Affine Parametric Varying Systems
      * Dissipativity of Affine Parametric Varying Systems
      * Hankel Norm of Affine Parameter Varying Systems
      * Positive Orthant Stabilizability
      * LMI For Stabilization Condition for Systems With Unsymmetrical Saturated Control
      * LMI Condition For Exponential Stability of Linear Systems With Interval Time-Varying Delays
      * Conic Sector Lemma
      * Polytopic Quadratic Stability
      * Mu Analysis
      * Optimization Over Affine Family of Linear Systems
      * Hurwitz Stabilizability
      * Quadratic Hurwitz Stabilization for Polytopic Systems
      * Output Energy Bound for Autonomous LTI Systems
      * Transient State Bound for Non-Autonomous LTI Systems
      * Transient Output Bound for Autonomous LTI Systems
      * Transient Output Bound for Non-Autonomous LTI Systems
      * Output Energy Bound for Non-Autonomous LTI Systems
# LMIs in Control/Stability Analysis/Continuous Time/D-Stability

      * Continuous Time D-Stability Observer