OpenLLM-France/wikimedia huggingface dataset:
# HKDSE Geography/M2a/Erosional Landforms
## (Interlocking spurs)

Interlocking spurs were not included in the curriculum and assessment guide. Only study the formation process if you have spare time. If not, simply remembering the name and appearance will do.
* Water in the upper course has little energy
* Thus it cannot remove obstacles in its path.
* Water flows around spurs instead of eroding them.
* This zig-zag movement of river flow forms interlocking spurs.

## Gorges

Example: Wu Xia
General:
* Downcutting along the channel forms V-shaped valleys
* Lateral erosion is rare
* Therefore, narrow, steep-sided valley - gorges - are formed.
By waterfall recession:
* The erosive power of waterfalls is great.
* When water erodes the backwall of a waterfall by hydraulic action and abrasion, it retreats.
* A deep valley is formed.
By uplift of land (less important):
* When land uplifts,
* vertical erosion occurs to form a V-shaped valley.
* A gorge is thus formed.

## Rapids

Example: Bride's Pool
* There are alternating layers of resistant and non-resistant rocks on the riverbed
* The river can vertically erode the non-resistant rocks (by hydraulic action and abrasion), but not resistant rocks. This is called differential erosion. A step-like riverbed is formed.
* The uneven bed causes turbulent currents called rapids.

## Potholes

Example: Near Bride's Pool
* At rapids, river flows over an uneven surface. When it meets and obstacle, it swirls and turbulence develops. An eddie is formed.
* If the riverbed is non-resistant/contains cracks, the load will drill circular hollows on the riverbed by abrasion. These are potholes.

## Waterfalls

* When a river flows down a slope, there is a strip of resistant rock (vertical, horizontal or dipping upstream) which is eroded very slowly
* The resistant rock in front will be eroded, and the flow of water will become more and more vertical
* Water will eventually fall vertically to form a waterfall
* Hydraulic action and abrasion undercut the base of the waterfall
* This creates a pool called a plunge pool
Note: As there is a sudden drop in river gradient, deposition occurs at the plunge pool. Boulders can be found there.
With internal processes (less important):
* A normal fault causes tensional force / A reverse fault causes compressional force
* The land slides vertically. A waterfall forms between the upper ground and the lower ground.
# HKDSE Geography/M1/Reasons for Stay
## Opportunities
### Power

Geothermal power can often be tapped along plate boundaries, where tectonic hazards are frequent. It is a are low-cost, highly efficient renewable energy source which produces little pollution and emits no greenhouse gases.
* Iceland
* 70% of Iceland's electricity is geothermal.

### Mining

Many rare and precious metals, gems and minerals are found in volcanic regions.
* Volcanic miners
* Iron, silver, copper, mercury and other important metals are found along plate boundaries, along with gems like manganese.

### Agriculture

Many volcanic regions have fertile soils because volcanic ash are rich in nutrients. When solidified lava are weathered and transported to farmlands, they also carry nutrients. This facilitates the growth of crops and increases yields, so farmers are attracted to settle there.

### Tourism

Hot springs (e.g. Japan) and geysers (e.g. Yellowstone National Park) often attract tourists. Hot springs are said to be beneficial to health. Volcanic and earthquake-prone areas like Mount Fuji, Hawaii and the Alps attract tourists because of scenic beauty. Thus tourism is important to the economies of hazard-prone regions. They tend to have a greater degree of economic development, attracting settlement.

### Other Opportunities

Benefits of living near coasts (mild climate, scenic beauty) are valid reasons for staying in tsunami-prone regions.

## Other Reasons

* Financial and political barriers prevent people from leaving
* People with social ties are unwilling to leave as they do not want to break their social network and have to rebuild one in a new place
* Historical factors: People tend to stay where much development has taken place
* Ancestral ties to one's homeland
* It is impossible to move to anywhere without hazards
# HKDSE Geography/M1/The Earth's Layers

The various layers of Earth are summed up below:
| Layer (by chemical composition) | Layer (by state) | Maximum depth |
| Crust (sial/sima) (1) | Solid lithosphere (4) | 30km |
| Mantle (Fe and Al) (2) | Solid lithosphere (4) | 100km |
| Mantle (Fe and Al) (2) | Plastic asthenosphere (5) | 640km |
| Mantle (Fe and Al) (2) | Solid lower mantle | 2800km |
| Core (Fe and Ni) (3) | Liquid outer core (6) | 4600km |
| Core (Fe and Ni) (3) | Solid inner core (7) | 6370km |

## Crust

The crust is a solid layer on the earth's surface. It includes continental and oceanic crusts.
| | Continental | Oceanic |
| Thickness | Thicker | Thinner |
| Density | Lighter | Denser and heavier |
| Composition | Sial - silica and aluminium | Sima - silica and magnesium |
| Geology | Mainly granitic | Mainly basaltic |
| Remarks | Includes continents and continental shelves | Includes continents and continental shelves |

## Mantle

It is denser, made of aluminium and iron, and divided into three parts.
| | Upper mantle | Upper mantle | Lower mantle |
| | Rigid mantle | Asthenopshere | Lower mantle |
| State | Solid | Liquid | Solid |
| Made of | Rocks | Magma | Rocks |

## Core

It is rich in iron and nickel. The outer core is a molten liquid. The inner core is a high-pressure solid.
# Handbook of Management Scales/Supplier quality management
## Supplier quality management (alpha = 0.84; composite reliability = 0.83)
### Description

Eight quality management practices were identiﬁed by the authors: customer focus, employee relations, management leadership, process management, product/service design, quality data and reporting, supplier quality management, and training.

### Items

* Extent to which long-term relationships are offered to suppliers. (0.56)
* Reduction in the number of suppliers since implementing just-in-time purchasing and/or total quality management. (0.61)
* Extent to which suppliers are evaluated according to quality, delivery performance, and price, in that order. (0.75)
* Extent to which suppliers are selected based on quality rather than price or delivery schedule. (0.75)
* Thoroughness of your organization’s supplier rating system. (0.74)
* Involvement of the supplier in your product/service development process. (0.64)
Items 1, 4–6 were adapted from Saraph et al. (1989); items 2 and 3 were developed by Kaynak (1997).

### Source

* Kaynak/Hartley (2008): A replication and extension of quality management into the supply chain. Journal of Operations Management, Vol. 26, No. 4, pp. 468–489.

### Related Scales

* Supplier development
* Supplier evaluation systems

## Supplier quality management (alpha = 0.78)
### Description

Through a detailed analysis of the literature, twelve constructs of integrated quality management strategies were identified: top management commitment, customer focus, supplier quality management, design quality management, benchmarking, SPC usage, internal quality information usage, employee empowerment, employee involvement, employee training, product quality, and supplier performance. Using a survey of 371 manufacturing firms, the constructs were then empirically tested and validated. For this purpose a confirmatory factor analysis approach was used.

### Items

Answer with respect to a critical component of the primary product.
* Quality is a more important criterion than price in selecting suppliers of the major component.
* Our supplier rating system considers the supplier’s engineering capability.
* Our supplier rating system considers the supplier’s financial stability.
* Our supplier rating system considers the supplier’s delivery performance.
* We provide technical assistance to our suppliers of this component.
* We are more interested in developing a long-term relationship with these suppliers than reducing prices.

### Source

* Ahire et al. (1996): Development and Validation of TQM Implementation Constructs. Decision Sciences, Vol. 27, No. 1, pp. 23-56.

### Related Scales

* Supplier development
* Supplier evaluation systems
# Handbook of Management Scales/Supply base reduction
## Supply base reduction (alpha = 0.65)
### Description

The authors identify key constructs related to supply chain management. Based on a systematic instrument develop process, they develop a set of reliable, valid, and unidimensional measurement scales.

### Items

* We rely on a small number of high quality suppliers. (0.57)
* We maintain close relationship with a limited pool of suppliers. (0.42)

### Source

* Chen/Paulraj (2004): Towards a theory of supply chain management: the constructs and measurements. Journal of Operations Management, Vol. 22, No. 2, pp. 119–150

### Comments

Only two items; relatively low factor loadings.
# Handbook of Management Scales/Supplier relationship
## Supplier relationship (alpha = 0.7398)
### Items

* We strive to establish long-term relationships with suppliers.
* Our suppliers are actively involved in our new product development process.
* Quality is our number one criterion in selecting suppliers.
* We rely on a small number of high quality suppliers.

### Source

* Flynn et al. (1994): A framework for quality management research and an associated measurement instrument. Journal of Operations Management, Vol. 11, No. 4, pp. 339-366.
# Handbook of Management Scales/Supply network structure
## Supply network structure (alpha = 0.82)
### Description

The authors identify key constructs related to supply chain management. Based on a systematic instrument develop process, they develop a set of reliable, valid, and unidimensional measurement scales.

### Items

* We have a permeable organizational boundary that facilitates better communication and/or relationship with our key suppliers. (0.59)
* Our relation with the suppliers is based on interdependence rather than power. (0.72)
* Our organizational structure can be characterized as a flexible value-adding network. (0.61)
* Our organizational/supply network structure does not involve power-based relationships. (0.78)

### Source

* Chen/Paulraj (2004): Towards a theory of supply chain management: the constructs and measurements. Journal of Operations Management, Vol. 22, No. 2, pp. 119–150
# Handbook of Management Scales/Supply base availability
## Supply base availability (alpha = 0.91)
### Items

* There were a lot of qualified and capable suppliers. (0.787)
* Many suppliers had the necessary capabilities to produce all items in the bundle. (0.915)
* Many suppliers possessed the required capacities. (0.922)

### Source

* Schoenherr/Mabert (2008): The use of bundling in B2B online reverse auctions. Journal of Operations Management, Vol. 26, No. 1, pp. 81-95.

### Comments

The central value of the Likert scale was 4. However, the mean values of the items are 4.778, 4.984, and 5.071, and thus larger than 4. It might therefore be recommended to use a more explicit wording (e.g. "a very high number of suppliers" instead of "many suppliers"). This could help to approach normal distributions.
# Handbook of Management Scales/Supply uncertainty
## Supply uncertainty (alpha = 0.88)
### Description

The authors identify key constructs related to supply chain management. Based on a systematic instrument develop process, they develop a set of reliable, valid, and unidimensional measurement scales.

### Items

* The suppliers consistently meet our requirements. (0.90)
* The suppliers produce materials with consistent quality. (0.88)

### Source

* Chen/Paulraj (2004): Towards a theory of supply chain management: the constructs and measurements. Journal of Operations Management, Vol. 22, No. 2, pp. 119–150

### Comments

Only two items were used to measure the construct. Additional items should be added.
# Handbook of Management Scales/Supplier performance improvement
## Supplier performance improvement (alpha = 0.83)
### Definition

A supplier’s operational performance refers to the combination of product development efficiency, process improvements, quality conformity, and short lead time (Womack et al., 1990). (For simplicity, the authors refer to this as performance.)

### Items

* In the last 2–3 years, we have continued to be able to improve product design performance through this partnership.
* In the last 2–3 years, we have continued to be able to improve process design through this partnership.
* In the last 2–3 years, we have continued to be able to improve product quality through this partnership.
* In the last 2–3 years, we have continued to reduce lead time through this partnership.

### Source

* Kotabe et al. (2002): Gaining from Vertical Partnerships: Knowledge Transfer, Relationship Duration, and Supplier Performance Improvement in the U.S. and Japanese Automotive Industries. Strategic Management Journal, Vol. 24, No. 4, pp. 293–316

### Comments

Based on the definition, the items can be interpreted as formative; for example, certain dimensions of performance (e.g., ecological performance) are missing and a reduction of lead time might contradict another performance goals (e.g., costs reduction).

### Related Scales

* See various performance-related scales in the Handbook of Management Scales.
# Handbook of Management Scales/Supply chain disruption orientation
## Supply chain disruption orientation (alpha = 0.82)
### Description

A scale to measure supply chain disruption orientation was adapted from Bode et al. (2011).

### Definition

Supply chain disruption orientation is characterized as the firm’s recognition and awareness of pending disruptions and how firms analyze and learn from prior disruptions (Bode et al., 2011).

### Items

* We feel the need to be alert for possible supply chain disruptions at all times. (0.67)
* Supply chain disruptions show us where we can improve. (0.72)
* We recognize that supply chain disruptions are always looming. (0.80)
* We think a lot about how a supply chain disruption could have been avoided. (0.74)
* After a supply chain disruption has occurred, it is analyzed thoroughly. (0.66)
(1 = disagree strongly, 7 = agree strongly)

### Source

* Ambulkar/Blackhurst/Grawe (2015): Firm’s resilience to supply chain disruptions: Scale development and empirical examination. Journal of Operations Management, Vol. 33–34, pp. 111–122

### Comments

The mean values ranged between 4.8 and 5.8. Given that a 7-point scale was used and thus mean values around would have been expected, future researchers could slightly adapt the items in order to shift the mean values closer to the center (e.g., “We strongly feel the need” rather than “We feel the need”).
# Handbook of Management Scales/Switching costs
## Switching costs (alpha = 0.78)
### Items

* When the contract with an application service provider is terminated, we can easily transfer to another provider.
* When the contract with an application service provider is terminated, we can easily manage the IT infrastructure ourselves.
* Once my firm is using application services, it is difficult to get rid of them. (reverse coded)

### Source

* Verwaal et al. (2009): Value Creation and Value Claiming in Strategic Outsourcing Decisions: A Resource Contingency Perspective. Journal of Management, Vol. 35, No. 2, pp. 420-444.

### Related Scales

* Asset specificity
* Specific assets
# Handbook of Management Scales/Task and work responsibilities
## Task and work responsibilities (alpha = 0.83)
### Description

The authors develop and validate a 16-item measure of i-deals negotiated by job incumbents across four content domains: task and work responsibilities, schedule flexibility, location flexibility and financial incentives.

### Definition

Idiosyncratic deals (i-deals) are "mutually beneficial, personalized agreements of a nonstandard nature that are negotiated between individual employees and their employers".
The task and work responsibilities dimension is associated with what employees do on their jobs.

### Items

* I have successfully asked for extra responsibilities that take advantage of the skills that I bring to the job. (0.77)
* At my request, my supervisor has assigned me tasks that better develop my skills. (0.76)
* I have negotiated with my supervisor for tasks that better fit my personality, skills, and abilities. (0.69)
* My supervisor has offered me opportunities to take on desired responsibilities outside of my formal job requirements. (0.61)
* In response to my distinctive contributions, my supervisor has granted me more flexibility in how I complete my job. (0.49)
* Following my initial appointment, my supervisor assigned me to a desirable position that makes use of my unique abilities. (0.43)

### Source

* Rosen et al. (2013): Let’s Make a Deal: Development and Validation of the Ex Post I-Deals Scale. Journal of Management, Vol. 39, No. 3, pp. 709–742

### Comments

The scale was tested across three samples; it can, thus, be assumed that it is valid and reliable. The content of the first four items is relatively similar. The factor loadings of the last two items are low.
# LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time Negative Imaginary Lemma
## The System

Given a square, discrete-time LTI system G: L$_{2e}$ --> L$_{2e}$ with state-space realization (A$_d$, B$_d$, C$_d$, D$_d$) where
$A_{d}\in \mathbb {R} ^{nxn}$, $B_{d}\in \mathbb {R} ^{nxm}$, $C_{d}\in \mathbb {R} ^{mxn}$, and $D_{d}\in \mathbb {R} ^{mxm}$.
In this system, $C_{d}(z1-A_{d})^{-1}B_{d}+D_{d}=B_{d}^{T}(z1-A_{d}^{T})^{-1}C_{d}^{T}+D_{d}^{T}$ and $det(1+A)\neq 0$ and $det(1-A)\neq 0$.

## The Data

$A_{d}\in \mathbb {R} ^{nxn}$, $B_{d}\in \mathbb {R} ^{nxm}$, $C_{d}\in \mathbb {R} ^{mxn}$, and $D_{d}\in \mathbb {R} ^{mxm}$

## The LMI:

The system G posed above is considered to be negative imaginary under either of the sufficient and necessary conditions:
* There exists $P\in \mathbb {S} ^{n}$, where P > 0 such that
$A_{d}^{T}PA_{d}-P\leq 0,$
$C_{d}+B_{d}^{T}(A_{d}^{T}-1)^{-1}P(A_{d}+1)=0$
2. There exists $Q\in \mathbb {S} ^{n}$, where Q > 0 such that
$A_{d}QA_{d}^{T}-Q\leq 0,$
$B_{d}+(A_{d}-1)^{-1}Q(A_{d}^{T}+1)C_{d}^{T}=0$

## Conclusion

By using the LMI described above, a discrete LTI system can be evaluated for the negative imaginary condition.

## Implementation

This LMI can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like MOSEK.

## Related LMIs

* Negative Imaginary Lemma

## External Links

* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
# LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time System Zeros With Feedthrough
## The System

Given a square, discrete-time LTI system G: L$_{2e}$ --> L$_{2e}$ with minimal state-space realization (A$_d$, B$_d$, C$_d$, D$_d$) where
$A_{d}\in \mathbb {R} ^{nxn}$, $B_{d}\in \mathbb {R} ^{nxm}$, $C_{d}\in \mathbb {R} ^{pxn}$, and $D_{d}\in \mathbb {R} ^{pxm}$ with m $\leq$ p. D$_d$ is full rank.
The transmission zeros of $G(z)=C_{d}(z1-A_{d})^{-1}B_{d}+D_{d}$ are the eigenvalues of: $A_{d}-B_{d}(D_{d}^{T}D_{d})^{-1}D_{d}^{T}C_{d}$.

## The Data

$A_{d}\in \mathbb {R} ^{nxn}$, $B_{d}\in \mathbb {R} ^{nxm}$, $C_{d}\in \mathbb {R} ^{pxn}$, and $D_{d}\in \mathbb {R} ^{pxm}$ with m $\leq$ p. D$_d$ is full rank.

## The LMI:

With the system defined above, it can be seen that G(z) is minimum phase if and only if there exists $P\in \mathbb {S} ^{n}$, where P > 0, such that:
${\begin{bmatrix}P&(A_{d}-B_{d}(D_{d}^{T}D_{d})^{-1}D_{d}^{T}C_{d})P\\*&P\end{bmatrix}}>0$.
If the system G is square (m = p), then full rank D$_d$ implies D$_d$$^{-1}$ exists and the above LMI simplifies to:
${\begin{bmatrix}P&(A_{d}-B_{d}D_{d}^{-1}C_{d})P\\*&P\end{bmatrix}}>0$.

## Conclusion

With the LMI constructed above, the system zeros for a discrete-time LTI system with feedthrough can be found and verified.

## Implementation

The LMI can be implemented using a platform like YALMIP along with an LMI solver such as MOSEK to compute the result.

## Related LMIs

* System Zeros without feedthrough
* System zeros with feedthrough

## External Links

* LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
# LMIs in Control/Matrix and LMI Properties and Tools/Frobenius Norm
## Frobenius Norm

Consider $A\in \mathbb {R} ^{n\times m}$ and $\gamma \in \mathbb {R}$$_{>0}$
The Frobenius norm of $A$ is $||A||$$_F$ =${\sqrt {tr(A^{T}A)}}={\sqrt {tr(AA^{T})}}$
The Frobenius norm is less than or equal to $\gamma$ if and only if any of the following equivalent conditions are satisfied.
1.There exists $S\in \mathbb {R} ^{n}$ such that
       ${\begin{bmatrix}Z&A^{T}\\*&1\\\end{bmatrix}}\geq 0,$
    ${\begin{aligned}\qquad tr(Z)\leq \gamma ^{\text{2}}.\qquad \\\end{aligned}}$
2.There exists $S\in \mathbb {R} ^{m}$ such that
       ${\begin{bmatrix}Z&A\\*&1\\\end{bmatrix}}\geq 0,$
    ${\begin{aligned}\qquad tr(Z)\leq \gamma ^{\text{2}}.\qquad \\\end{aligned}}$

## External Links

* LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
# LMIs in Control/Matrix and LMI Properties and Tools/Generalized Negative Imaginary Lemma
## Introduction

These systems are often related to systems involving energy dissipation. But the standard Positive real theory will not be helpful in establishing closed-loop stability. However, transfer functions of systems with a degree more than one can be satisfied with the negative imaginary conditions for all frequency values and such systems are called systems with negative imaginary frequency response.

## The System

Consider a square continuous time Linear Time invariant system, with the state space realization $(A,B,C,D)$
    ${\begin{aligned}{\dot {x}}(t)=Ax(t)+Bu(t)\\y=Cx(t)+Du(t)\end{aligned}}$

## The Data

$A\in \mathbb {R} ^{n\times n},B\in \mathbb {R} ^{n\times m},C\in \mathbb {R} ^{m\times n},D\in \mathbb {S} ^{m}$

## The LMI

Consider an NI transfer matrix G$_1$(s) and an SNI transfer matrix G$_2$(s) = C$_2$(s1 - A$_2$)$^{-1}$ B$_2$ + D$_2$. The condition λ̅ (G$_1$(0)G$_2$(0) < 1 is satisfied if and only if
                      S$^T$(-C$_2$A$_2$$^{-1}$B$_2$ + D$_2$)S < 1,

## Conclusion

The above equation holds true if and only if S S$^T$ = G$_1$(0).

## Implementation

This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.

## Related LMIs

* Negative Imaginary Lemma