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Optimization and Hessian Matrix Calculations

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syms K L

[K,L]=meshgrid(0:0.1:10);
Q=10*(K1/4)*(L1/2);
mesh(K,L,Q)
contour(K,L,Q)
meshc(K,L,Q)
syms K L;
Q=10*(K1/4)*(L1/2);
diff(Q,K)
hessiana=jacobian(jacobian(Q,[K,L]),[K,L])
subs(hessiana,[K,L],[2,1])


syms x y;
f=4*x2+y2+2*x*y-3*x-y+1;
[x,y]=solve(diff(f,x),diff(f,y),x,y)
syms x y;
hessiana=jacobian(jacobian(f,[x,y]),[x,y])
eig(hessiana)
vpa(ans)


syms x y lambda;
f=x2+y2-2*x-x*y+5;
L=f-lambda*(x+y-1);
[lambda,x,y]=solve(diff(L,lambda),diff(L,x),diff(L,y),lambda,x,y)
 syms x y lambda;
hessiana=jacobian(jacobian(L,[x,y]),[x,y])
eig(hessiana)

Essential Digital Marketing Terms Explained

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Understanding Key Digital Marketing Concepts

Search Engine Marketing (SEM)

Search Engine Marketing (SEM) is a process that utilizes multiple methods to improve market visibility and exposure for a brand, product, or service.

Search Engine Advertising (SEA)

Search Engine Advertising (SEA) allows you to directly display your paid advertisements among the search results on various search engines, such as Google, Bing, and Yahoo.

Content Marketing

Content Marketing is a type of marketing that involves the creation and sharing of online material (such as videos, blogs, and social media posts) that does not explicitly promote a brand, but is intended to stimulate interest in its products or services.

Press Release

A Press Release is a written or recorded... Continue reading "Essential Digital Marketing Terms Explained" »

Ordinal Numbers in English: From 1st to 100th

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1 - 20

  • 1 (one) → 1st (first)
  • 2 (two) → 2nd (second)
  • 3 (three) → 3rd (third)
  • 4 (four) → 4th (fourth)
  • 5 (five) → 5th (fifth)
  • 6 (six) → 6th (sixth)
  • 7 (seven) → 7th (seventh)
  • 8 (eight) → 8th (eighth)
  • 9 (nine) → 9th (ninth)
  • 10 (ten) → 10th (tenth)
  • 11 (eleven) → 11th (eleventh)
  • 12 (twelve) → 12th (twelfth)
  • 13 (thirteen) → 13th (thirteenth)
  • 14 (fourteen) → 14th (fourteenth)
  • 15 (fifteen) → 15th (fifteenth)
  • 16 (sixteen) → 16th (sixteenth)
  • 17 (seventeen) → 17th (seventeenth)
  • 18 (eighteen) → 18th (eighteenth)
  • 19 (nineteen) → 19th (nineteenth)
  • 20 (twenty) → 20th (twentieth)

21 - 30

  • 21 (twenty-one) → 21st (twenty-first)
  • 22 (twenty-two) → 22nd (twenty-second)
  • 23 (twenty-three) → 23rd (twenty-third)
  • 24 (twenty-four) → 24th (twenty-fourth)
... Continue reading "Ordinal Numbers in English: From 1st to 100th" »

Quality Management Principles: Deming, PDCA & SPC

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1.1 Defining Quality: Performance and Expectations

Quality = Performance (how it works) / Expectations. If Q > 1, the customer has a positive feeling. The customer determines his or her expectations.

Definition of quality: A group of properties and characteristics of a service or a product that has the ability to satisfy different needs. Some dimensions of quality are reliability, durability, service, reputation, and more. These dimensions are independent.

  • Performance — how well the product or service works.
  • Expectations — what the customer anticipates or requires.
  • Dimensions of quality — reliability, durability, service, reputation, etc.

1.2 Enemies of Quality and Cultural Changes

Common enemies of quality include:

  • Lack of definition: Responsibilities
... Continue reading "Quality Management Principles: Deming, PDCA & SPC" »

Air Transport Association Codes and Special Passenger Requirements

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International Air Transport Association (IATA)

IATA is the International Air Transport Association, a trade association for the world’s airlines. It promotes cooperation, safety, reliability, confidence, and economy in air transport, benefiting its private shareholders.

  • IATA represents 290 airlines, accounting for 82% of worldwide air traffic.
  • It was established in 1945 in Havana, Cuba.
  • IATA seeks common solutions for industry problems that individual airlines cannot solve alone.

IATA Airport and Airline Codes

  • IATA Airport Codes: These are 3-letter codes used to designate airports worldwide.
  • Cities with multiple airports also have a specific code to designate the city itself (e.g., NYC for New York City).
  • Airline Designators:
    • IATA codes (2 letters)
... Continue reading "Air Transport Association Codes and Special Passenger Requirements" »

Core Business Functions and Decision-Making Strategies

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Understanding the Business Entity

A company is an entity whose primary purpose is to obtain benefits through the sale of goods and services on the market.

1. Functions in the Organization

Management involves four core functions:

  • Planning: Setting goals and defining the path to achieve them through a Strategic Plan, including:
    • Resources
    • Actions
    • People
    • Control
  • Organizational Function: The implementation of the established plan.
  • Leadership Function: Overseeing employee work and influencing performance by:
    • Leading towards goals
    • Motivating staff
    • Understanding problems
    • Transmitting the business plan
    • Providing instructions
  • Control Function: Monitoring progress and implementing corrective measures when deviations occur.

Departmental Structure

A department consists of... Continue reading "Core Business Functions and Decision-Making Strategies" »

Formal vs. Non-Formal Education Systems and Characteristics

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Formal Education Systems

Formal education corresponds to a systematic, organized education model, structured and administered according to a given set of laws and norms. It typically presents a rather rigid curriculum regarding objectives, content, and methodology.

Key Characteristics of Formal Education

It is characterized by a contiguous education process, named, as Sarramona remarks, “presential education,” which necessarily involves the teacher, the students, and the institution.

It corresponds to the education process normally adopted by our schools and universities. Formal education institutions are administratively, physically, and curricularly organized and require students to maintain a minimum classroom attendance.

It confers degrees... Continue reading "Formal vs. Non-Formal Education Systems and Characteristics" »

Automatic Voltage Control and Generation Control in Power Systems

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Automatic Voltage Control

Basically consists of a main exciter field which excites the alternator field to control the output voltage. The exciter field is automatically controlled through an error equal to V reference - Vt. When the output voltage is higher than the required value, the BT is measured by a potential transformer and fed back to the input so that the error V reference - Vt is applied to the exciting field. This ensures that the generator output voltage is maintained at the desired level.

Components:

  • Potential Transformer: Provides a sample of terminal voltage
  • Differentiating Device: Gives actuating error e = V ref - Vt
  • Error Amplifier: Amplifies the error signal
  • SCR Power Amp: Transfer Function = (ke / 1 + TeS)

Automatic Generation

... Continue reading "Automatic Voltage Control and Generation Control in Power Systems" »

Essential Weather Measurements: Humidity and Wind Dynamics

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Relative Humidity: Definition and Measurement

Relative humidity (RH) relates the amount of moisture actually present in the atmosphere to the maximum amount it can hold at a given temperature. If the air is saturated, the relative humidity is 100%.

Measuring Relative Humidity with a Hygrometer

Relative humidity is measured using a wet and dry bulb thermometer, sometimes known as a hygrometer. The measurement process relies on evaporative cooling:

  • Water from a bottle soaks the cotton gauze covering the wet bulb, keeping the thermometer wet.
  • As water evaporates from the damp cotton, it cools and reduces the temperature of the wet bulb thermometer.
  • Consequently, the wet bulb temperature is lower than the dry bulb temperature due to this cooling effect.
... Continue reading "Essential Weather Measurements: Humidity and Wind Dynamics" »

Service Marketing: Essential Concepts and Strategies

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What is the Service Marketing Mix?

All elements within the control of the firm that communicate the firm's capabilities and image to customers or that influence customer satisfaction with the firm's product and services: product, price, place, and promotion.

  • People: All human actors who play a part in service delivery and thus influence the buyer's perceptions: namely, the firm's personnel, the customer, and other customers in the service environment.
  • Physical Evidence: The environment in which the service is delivered and where the firm and customer interact, and any tangible components that facilitate performance or communication of the service.
  • Process: The actual procedures, mechanisms, and flow of activities by which the service is delivered
... Continue reading "Service Marketing: Essential Concepts and Strategies" »