Notes, abstracts, papers, exams and problems of Mathematics

Fortran 90: Implicit None and Vector Management

Implicit None

In Fortran 90, undeclared variables starting with I, J, K, L, or M are treated as integers, while others are treated as real numbers. However, it's best practice to avoid implicit declarations. Use IMPLICIT NONE right after the program instructions to disable implicit typing. This forces you to explicitly declare all variables, preventing potential errors due to character misuse.

Vector Management Forms

Ordering one-dimensional arrays (vectors) is a common operation. Here are three simple methods: selection, insertion, and bubble sort.

In all cases, we'll assume a one-dimensional array of N elements.

Selection Sort

1. Find the smallest element in the vector.
2. Swap it with the element in the

Joint Cost Allocation Methods

Joint costs are costs of a production process that yields multiple products (co-products). Here's a breakdown of common allocation methods:

Criterion: Market Value

This method allocates joint costs based on the relative sales value of each co-product. Here's how it works:

1. Calculate Total Sales Value:
   • List each co-product (e.g., A, B, C).
   • Determine the sales value per unit (e.g., per kg).
   • Determine the quantity of each co-product produced (e.g., in kg).
   • Multiply the sales value per unit by the quantity to find the total sales value for each co-product.
2. Distribute Total Joint Costs:
   • Calculate the total sales value of all co-products.
   • For each co-product, divide its total sales value by the total sales value of all co-products.

Fundamentals of Statistical Analysis

Frequency Distribution

Ungrouped Data

Ungrouped data are lists of observed values when the pooled data represent a mass of observed data.

Pooled Data

When data are grouped in a frequency distribution.

• Collect data and make a tally sheet

Determination of Range

The range is the difference between the highest observed value and the lowest value observed.

Determining the Range of Classes

The range of classes is the enactment between the midpoint of classes.

Determine the Midpoints of the Class

The midpoint of the class must include the minimum data value in that class.

Determine the Class Boundaries

The class limits are the extreme values or limits of a class and are called the upper limit and lower limit.

Identify the Frequency

Grounded Theory: Strategies and Methods

Grounded theory has two main strategies:

Theoretical Sampling

Involves adding to the sample of subjects or situations encountered, additional comments, or further interviews. It seeks to find different cases.

Constant Comparative Method

It is a method to analyze the data at different times in which the researcher interacts with:

1. Classified portions of data:
   • Words
   • Phrases
   • Paragraphs

Categories arise, either intuited or implicit (they are marked, but without a name).

Constant Comparative Method

As the process of selecting pieces of data advances, categories appear with more explicit rules.

The task is to identify:

1. Emerging categories = Issues
   • Categories = Properties
2. Central category = Recurring Themes

Links between categories... Continue reading "Grounded Theory: Strategies, Methods, and Analysis" »

**Purchase Operations**

Shopping is any transaction by which a person receives the domain of property for valuable consideration. The purchase consists of two stages or operations:

**Request for Purchase or Requisition of Goods**

This is a formal request made by a department or warehouse operations, being directed to the purchasing department.

**Order Form**

The purchasing department receives the application and analyzes the real need, according to the financial situation and market conditions, as the article refers.

**Reception Guide**

This is a document issued by the warehouse when it acquires the goods from suppliers. Prior to the receipt, the warehouse manager must take care to verify if the merchandise received matches the packing list issued... Continue reading "Purchase and Sales Operations: Essential Documents" »

Key Warehouse Functions

Departure

• Monitor the consumption of items by various departments.
• Suitably distribute articles.

Entry

• Reject material that does not meet the requirements of the order.
• Monitor and handle the exchange of expired material.

Storage

• Protect and oversee all the products stored.
• Register and control the movements of stock.
• Avoid losses in the stored materials.
• Ensure items are consumed before the expiry date.
• Design documents necessary for good control of the warehouse.
• Request resupply when stocks are minimal.

When to Start Product Replacement

Replacement of a product should start before falling below the minimum stock.

High Maximum Stock: Advantages and Disadvantages

Maximum stock refers to the maximum amount of a particular item above... Continue reading "Warehouse Functions and Inventory Management in Healthcare" »

VAT Fees Eligible for Deduction

The following fees can be deducted:

• Submission-entry of goods from another taxable person
• Imports of goods
• Intra-Community acquisitions
• Fees relating to cases of reverse charge

Partial Deduction or Pro Rata

This applies when a company performs two types of activities: operations with deduction and operations without deduction.

The consequence is that only a portion or percentage of the taxes charged can be deducted.

What percentage? To determine the coefficient, calculate the following:

(Sum of output-delivery deduction in the year) / (Sum of all delivery-end of the year)

To calculate the deduction, multiply the percentage by the taxes charged.

Dynamics During the Exercise: Provisionally apply the percentage from the previous... Continue reading "VAT Deduction Rules: Fees, Partial Deduction, and Investment" »

Frequency Distribution

1) Loose Data: Data collected that has not been organized numerically. For example, heights of males and females obtained from a survey, arranged alphabetically.

2) Ordination: An arrangement of numerical data in ascending or descending order. The difference between the largest and smallest number is called the data range.

Example:

Data Management Data Range
2.1 1 A: 10 to 1
7.6 2 R: 9
4.9 4
8.10 6 R: range of the data.
7
8
9
10

3) Frequency Distribution: When dealing with large amounts of loose data, it's useful to distribute them into classes or categories and determine the number of individuals belonging to each category, often called a class.

A tabular distribution of data by type or category with its corresponding... Continue reading "Understanding Frequency Distributions: Data Organization" »

Business Documents

Commercial documents, also called "proof," constitute the evidence of any business operation conducted by a company. Thus, each proof tests a type of transaction. It is known that any operation involves at least two parts. For each of them, it will have a different meaning (as discussed later: buyer or seller, debtor or creditor, or collector payer, etc.).

Understanding Mathematical Competence

Mathematical competence is the ability to use and relate numbers, basic operations, and forms of expression and mathematical reasoning. This skill is used both to produce and interpret different types of information, to expand knowledge on quantitative and spatial aspects of reality, and to resolve problems related to everyday life and the workplace.

Components of Mathematical Competence

Mathematical competence (Comp) is part of the ability to interpret and express with clarity and precision information, data, and arguments. This competency:

• Increases the real possibility to continue learning throughout life, both within and outside of school.
• Favors effective participation in social life.

This competition also... Continue reading "Understanding Mathematical Competence in Everyday Life" »