TECTechnics - Follow And You Shall Never Thirst For Knowledge

Its All About PjProblemStrings (S_iP_jA_jk). A Space of Interest S_i, PjProblem Of Interest P_j And Its Allelle, A_jk
For Knowledge Sake. One Code (S_iP_jA_jk) For All Knowledge. Follow And You Shall Never Thirst For Knowledge

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Pj ProblemStrings Sequencing

On a Tripod in the Kingdom of Conceptual Knowledge, rest all concepts in the physical Universe. Triadic Time; Existential Triad and Pj ProblemStrings Sequencing are the three legs of the Tripod. We have addressed Triadic Time and Existential Triad. The focus is now on PjProblemStrings Sequencing.

The TECian Space - Thinking With Numbers

In the final analysis everything reduces to numbers. So is the TECian Space, the final concept of the TECTechnics Theory. The TECian Space reduces all problems of a given space to a conceptual space of only two digits taken from the universal knowledge code (S_iP_jA_jk).....continue

Digging Air - The PjProblemStrings Sequences

Digging Air

Land, water and air. A lot of digging going on. All three have dual traits: they are both destroyers and benefactors.
(a) Earth's atmosphere is what is called air. Briefly highlight the origin of Earth's air.
(b) Do you agree that air is the least resistive to digging when compared to land and water diggings in equivalent amounts? Why?
(c) Give at least one example of how air as a destroyer is manifested by digging air.
(d) Give at least one example of how air as a benefactor is manifested by digging air.
(e) The illustration shows a bird flying. Indicate the PjProblemstrings Sequence for the flight.
(f) In Digging Earth, and Digging Water, the following PjProblemStrings Sequence represented a simple digging of earth (lithosphere) by a bulldozer and bailing water:
S₇P₁A₁₇S₇P₂A₂₁S₇P₃A₃₂S₇P₃A₃₁S₇P₄A₄₁S₇P₄A₄₂S₇P₄A₄₂S₇P₄A₄₁
Some PjProblem Strings not directly influencing the digging are implied. For example, the equlibrium of the operator and the bulldozer, the grouping/interaction and equilibrium of the earth dumped.
Identify a similar simple digging of air? How does the pjproblemstrings sequences of this simple digging of air differ from the simple digging of earth and the simple digging of water?
(g) What is the primary difference between the simple digging of air and the simple digging of earth (lithosphere) and the simple digging of water represented by the PjProblemStrings Sequence indicated in problem (f)?
(h) What is the difference between buoyancy and the digging of air?
(i) Explain the correctness or incorrectness of the following assertion: every movement in air is digging
(j) Why must living things dig?

→ Solution: the strings and the math.

Digging Water - The PjProblemStrings Sequences

Digging Water

Omi o l'ọta (Yoruba for water has no enemy) is perhaps the most profound song of the great musical mind, Fẹla Anikulapọ Kuti. In the song, Fẹla sang about the indispensability of water even when water is the cause of one's sorrow. Water as a destroyer and water as a benefactor constitute the dichotomous duality of the character of water. This duality is manifested by digging water.
(a) Most of Earth is water. Briefly highlight the origin of water on Earth.
(b) Give at least one example of how water as a destroyer is manifested by digging water.
(c) Give at least one example of how water as a benefactor is manifested by digging water.
(d) The illustrations shown are of a hippo relaxing in water and of ducks swimming. Indicate the PjProblemstrings Sequence for each illustration.
(e) In Digging Earth, the following PjProblemStrings Sequence represented a simple digging of earth (lithosphere) by a bulldozer:
S₇P₁A₁₇S₇P₂A₂₁S₇P₃A₃₂S₇P₃A₃₁S₇P₄A₄₁S₇P₄A₄₂S₇P₄A₄₂S₇P₄A₄₁
Some PjProblem Strings not directly influencing the digging are implied. For example, the equlibrium of the operator and the bulldozer, the grouping/interaction and equilibrium of the earth dumped.
If earth is replaced by water and the bulldozer is replaced by an appropriate tool, What is the common name for this simple digging of water.
(f) What is the primary visible difference between the simple digging of earth (lithosphere) and the simple digging of water represented by the PjProblemStrings Sequence indicated in problem (e)?
(g) What is the difference between buoyancy and the digging of water?
(h) Explain the correctness or incorrectness of the following assertion: every movement on or in water is digging

→ Solution: the strings and the math.

Time, Frequency And Complex Frequency Domains - The PjProblemStrings Sequences

Time, Frequency And Complex Frequency Domains

Analyses of sinusoidal excitations of orders greater than two, are not simple. There are various computer programs that aid in the analyses. Nonetheless, it is very important that one grasps the mathematical tools used to simplify the analyses of sinusiods in the time domain where they exist.
(a) Given that the time, frequency and complex frequency domains are associated with the containerships of sinusoidal excitations; indicate the general identity of a sinusoidal excitation in each of the domains.
(b) What mathematical tools are used to arrive at the general identities of sinusoidal excitations in the frequency and complex frequency domains?
(c) Given an arbitrary sinusoidal excitation in the time domain, derive its representation in the frequency and complex frequency domains. Thus establish the PJProblemStrings Sequence of the domain switch of a sinusoidal excitation.
(d) Determine the complex frequencies that are associated with:
(i) 5e^-4t (ii) cos2ωt (iii) sin (ωt + 2θ)
(iv) 4e^-2tsin(3t - 50^o) (v) e^-3t(2 + cos4t)
(e) Determine the complex frequency s and V(s) associated with:
(i) 5e^-2t (ii) 5e^-2tcos(4t + 10^o) (iii) 4cos(2t - 20^o)
(f) Determine v(t) if:
(i) s = -2, V = 2<0^o (ii) s = j2, V = 12<-30^o (iii) s = -4 + j3, V = 6<10^o
(g) Determine the Laplace transform of the following functions:
(i) e^-atsin(ωt)u(t) (ii) e^-atcos(ωt)u(t)

→ Solution: the strings and the math.

Coding - IPO - The PjProblemStrings Sequences

A Simple C++ Swap Code: swap()

01: #include <iostream>
02:
03: using namespace std;
04: void swap(int &x, int &y);
05:
06: int main()
07: {
08:     int x = 5, int y = 10;
09:
10:     cout << "Main. Before swap, x: " << x << " y:" << y << end 1;
11:    //...

IPO (Initial Public Offering) is a familiar acronym in the investment space. It usually comes into play when a private company is going public and its stocks have to be distributed as shares amongst investors. In many other contexts, IPO is the acronym for the powerful triadic concepts of Input-Processing-Output. Coding is all about IPO.
(a) What other activities can be summarized by the IPO acronym?
(b) What constitute Input, Processing and Output in coding?
(c) Describe the given C++ swap code with respect to its objective and its IPO.
(d) Indicate the PjProblem Strings associated with its IPO. Thus establish the PJProblemStrings Sequences of the code.

→ Solution: the strings and the math.

Electric Circuit Of A Lab Power Supply - The PjProblemStrings Sequences

Circuit Of Lab Power Supply

The electron is existentially indispensable. It is at the heart of chemical reactions; and the electrical energy that propelled humans into their unique technological sphere of influence. The electron will also play a fundamental role in homo -sapiens series' journey towards infinite intelligence.

Figure 7.7 is an electric circuit of a lab power supply put together in the TECTechnics Lab. Space of interest : S₇P₁A₁₄ (1' by 1' by 4" container)
(a) Define: (i) electricity (ii) voltage (iii) resistance (iv) electric circuit.
(b) Identify the components of the circuit and their respective functions in the circuit.
(c) What are the three primary stages of the circuit? What are the PjProblem Strings associated with each of the stages? Thus establish the PjProblem String Sequences of the lab power supply.

→ Solution: the strings and the math.

Words Are Numbers - The PjProblemStrings Sequences

The following sequences of prime numbers represent three different four letter words:

(i) 1337195
(ii) 21135225
(iii) 35233115

Determine the PjProblemStrings sequence used to establish the sequences of prime numbers as words. Then indicate the words the above sequences of prime numbers represent.

→ Solution: the strings and the math.

Amino Acids - The PjProblemStrings Sequences

Amino Acids Sequences

X and Y are amino acids, Z is an amino acid sequence.
(a) What is an amino acid?
(b) What is a protein?
(c) Identify X and Y of figure 7.
(d) Given that the space of interest is the human body, and based on the identities you established in (c), describe the reaction X + Y -------> Z of figure 7. Thus establish the PjProblemStrings Sequences of Amino Acids.
(e) What is the relationship between genes and amino acids?
(f) List the 20 amino acids found in most proteins.
(g) List the ten essential amino acids. Which of these amino acids can be produced in the body?
(h) Are all the 20 amino acids found in the body compounds of only carbon, hydrogen, nitrogen and oxygen?
(i) What distinguishes one protein from another?
(j) List some fundamental and important functions of proteins.

→ Solution: the strings and the math.

Venn Diagram - The PjProblemStrings Sequences

The Venn Diagram (named after John Venn who invented it), is a basic model generally used to group members of two or more different sets. In particular, it highlights unique groups of sets and the members common to the groups.
A probabilistic view of the Venn Diagram sees the Venn Diagram as an outcome space consisting of probable event spaces resulting from a random experiment. It is this view that is the focus here.

(ai) What is a random experiment? (ii) What is an outcome space? (iii) What is an event?
(b) Is the Universe an outcome Space? Explain.
(c) Is an empy space an outcome space?
(d) Highlight the key aspects of the Venn Diagram
(e) Asssign PjProblemStrings to your highlights in (d). Thus establish the PjProblemString Sequences.
(f) Suppose state X has a northern region (NR), a central region (CR) and a southern region (SR). The following percentages is from X's department of housing:
28 % of X's residents own houses in NR
30 % of X's residents own houses in CR
18 % of X's residents own houses in SR
14 % of X's residents own houses in NR and CR
12 % of X's residents own houses in NR and SR
10 % of X's residents own houses in CR and SR
8 % of X's residents own houses in all three regions
What % of X's residents do not own houses in the state?

(g) The illustrated Venn Diagram focuses on two and three event spaces and their intersections. Can the Venn Diagram be used to illustrate four or more event spaces and their intersections?
(h) Give an example of an outcome space with four or more event spaces that intersect.

→ Solution: the strings and the math.

Digging - The PjProblemStrings Sequences

Digging

One of the ways humans derive benefits from the earth is to dig it. They dig earth to sow; they dig it to build; they dig it to mine; they dig it to hide valuables and they dig it to bury their loved ones.
(a) The illustrated bulldozer is engaged in simple digging. Highlight its digging.
(b) Indicate the PjProblem Strings for the highlights. Thus establish the PjProblemStrings Sequences for the digging.
Other livings things are also diggers: some rodents dig to hibernate (e.g. the groundhog); bears dig to find food; dogs dig when hot in search of cool space; squirrels dig to hide their food and trees dig in search of water and nutrients.
(c) How does the digging of a tree differ from the digging of the illustrated bulldozer.
(d) Do you agree that walking on sand is digging? If you do, differentiate the digging that results from walking on sand from the digging of the illustrated bulldozer.
(e) Suggest two prerequisites one would need inorder to formulate a mathematical model for the digging of the bulldozer.
(f) Explain the correctness or incorrectness of the following assertion: every movement on the ground is digging.

→ Solution: the strings and the math.

Life Of A Celestial Star - PjProblemStrings Sequences

Celestial stars influenced the creation of the natural elements that constitute living things on earth. The Sun, which is the nearest star to earth, continues to influence existence of living things on earth.
(a) Highlight the life of a star from birth to death.
(b) How did the distribution of nebulae in Space aid the formation of stars?
(c) List four descriptions that together establish the identity of a star.
(d) Each stage in the life of a star was influenced by one or more of the fundamental forces of nature. Which two fundamental forces are critical to the onset of fusion in a star?
(e) Which motions that occur during the last phase of a star's life are mostly responsible for the formation of higher mass elements beyond Iron (Fe)?
(f) The early Universe primarily contained Hygrogen and Helium. Stars made the formation of more elements possible. So they played an important role in the formation of Earth and its inhabitants. True or False
(g) Stars are grouped into 7 classes (O,B,A,F,G,K,M) according to surface temperature. Where O is the hottest and M is the coldest.The main sequence is a band of stars indicated in a Hertzsprung-Russell color - brightness plot (H-R diagram). Given a main sequence star that belongs to the M group. Approximate its maximum surface temperature, conventional color, apparent color, mass in solar mass, luminosity in solar luminosity and the nuclei being fused in its core.
(h) List some of the celestial bodies that are conclusive evidence of the death of a star.
(i) Indicate the PjProblestrings for each of the highlights in (a). Thus establish the PjProblemstrings Sequences for the life of a celestial star.

→ Solution: the strings and the math.

PjProblemStrings Sequences Of The Early Universe

PjProblemStrings Sequencing Of The Early Universe

At about time t = 10¹³ secs (300,000 yrs), the Universe was emerging from its early beginnings. The atom became the most stable matter about this time.
(a) Highlight the journey of the early Universe from time t = 0 secs to time t = 10¹³ secs.
(b) Why did the Universe not contain atoms, even though protons, neutron and electrons were present from t=10² to t=10¹³?
(c) What atoms were formed during the process called recombination?
(d) Which forces were responsible for the protons-protons bonding, and the protons-electrons attraction that made the formation of atoms possible?
(e) What is the principal atomic motion that resulted from the success of recombination?
(f) Recombination cleared travel-paths for photons(light's sub particles). Consequently, photons were able to travel freely and farther. A change that made knowledge of the universe possible. True or False?
(g) Our world is made up of Quarks (protons, neutrons) and Leptons (electrons, muons, taus). We can observe in the everyday world, only up and down quarks, electrons and electron-neutrinos. These particles are called first generation particles.
Group these interactions: proton-proton; proton-neutron; proton-electron?
(h) What was the most stable matter in the Universe when it was about 300,001 yrs old?
(i) Describe the PjProblemStrings for each of the highlights in (a). Thus establish the PjProblemStrings Sequences of the early Universe.

→ Solution: the strings and the math.

PjProblemStrings Sequences Of Triadic Algebra

PjProblemStrings Sequences Of Triadic Algebra
The term Algebra was derived from Al-Jabr wal-Muqobalah:
The Compedious Book Of Calculation By Completion And Balancing
written by the great mathematician Mohammed ibn Musa al-Khowarizmi (A.D. 780 - 850).

(a) What is the meaning of Triadic Algebra?
(b) Explain the three concepts that constitute Triadic Algebra
(c) Describe the PjProblemStrings Sequences that represent
the three concepts of Triadic Algebra.

→ Solution: the strings and the math.

PjProblemStrings Sequencing And The Derivative

PjProblemStrings Sequencing and The Derivative

The derivatives and anti-derivatives of functions are very important analytical tools. They form the branch of mathematics generally known as calculus. Calculus has been and continue to be an indispensable tool in the analysis of existential problems. The great Isaac Newton (1642-1727 A.D.) formulated the calculus. He called his formulation the method of Fluxions.

(a) What work does the derivative do?
(b) Use PjProblemStrings Sequencing to broadly describe this work of the derivative.
(c) What is the geometric interpretation of the derivative of a single variable function and a multi-variable function.
(d) Is the geometric interpretation consistent with PjProblemStrings Sequencing?
(e) What are some of the applications of the derivative?

→ Solution: the strings and the math.

PjProblemStrings Sequences Of Information Supply Chains In The Human Body

PjProblemStrings Sequences Of Information Supply Chains In The Human Body

Timely information (particularly in living organisms) is an existential demand. So, there exist existential information supply chains.

(a) What is information?
(bi) In what primary forms is information transmitted in the human body?
(ii) Identify the information supply chains in the human body.
(iii) Indicate the PjProblemStrings Sequences of the information supply chains.
(iv) Which of the 7 types of PjProblemStrings Sequences are present in the information supply chains in the human body?
(ci) How has the human body secured its information supply chains?
(ii) Is the security perfect?
(iii) What lessons can humans learn from how information supply chains are secured in the human body?
(di) Name some important hormones, the information they contain and the glands that secrete them in the human body.
(ii) Name the organs that receive the hormonal information named in (di) and describe how they respond to the information
(e) Briefly state the fundamental biologic cycle of information.
(fi) How is the information supply chains of the human body similar to the information supply chains called the internet.
(fii) How is the information supply chains of the human body dissimilar to the information supply chains called the internet.

→ Solution: the strings and the math.

PjProblemStrings Sequences Of Adenosine Triphosphate (ATP) Supply Chains

PjProblemStrings Sequences Of ATP Supply Chains

Energy is the basic existential currency especially for living organisms. In other words, existence demand energy. So, there exist existential supply chains.

(a) What is Adenosine Triphosphate (ATP)?
(bi) Where in the human cell is ATP produced?
(ii) Identify the supply chains needed to produce ATP in the human body.
(iii) Indicate the PjProblemStrings Sequences of the supply chains.
(iv) Which of the 7 types of PjProblemStrings sequences are present in ATP supply chains?
(ci) How has the human body secured its ATP supply chains?
(ii) Is the security perfect?
(iii) What lessons can humans learn from how ATP supply chains are secured in the human body?
(d) ATP is a single nucleotide. Name two important macromolecules in the human body that also contain nucleotides.
(e) How is the energy ATP stores made available in cells?
(f) Briefly state the fundamental biologic cycle of energy.

→ Solution: the strings and the math.

PjProblemStrings Sequences Of Supply Chains

PjProblemStrings Sequencing Of Supply Chains

Any being has at least one basic need at creation. These basic needs are natural demands of the being. Natural demands must be met by supply chains. In other words, natural demands and the supply chains that meet them are existential imperatives necessary for the maintenance of existential equilibrium. Over time, humans have created various demands beyond those incorporated in them at creation. Consequently, there exist various supply chains. However, most human supply chains cater to humans' natural demands and mutants of the demands.

Supply chains are at the heart of existence and they are configurations of PjProblemStrings Sequences.

(a) Name two primary natural demands required by living things on earth and indicate the supply chains for the demands.
(bi) Identify two primary supply chains in the human body and indicate the demands they meet.
(ii) Identify the forces and the motions of the PjProblemStrings Sequences of the supply chains.
(ci) Land ports, sea ports, air ports (and in the future, space ports) are supply chains. Indicate the demands they meet.
(ii) Which of the seven types of PjProblemStrings Sequences are commonly seen at airports? Which types are rarely seen?
(di) Figure 177 is a sketch of part of the supply chains of the super market with H as headquarters, D1 and D2 as depot, D11, D12, D13, D21, D22, D23 as individual stores. B is the supermarket's bank that links H to banks network. Why is it easy to see in figure 177 that H is the head office (or headquarters)?
(ii) What part of the supply chains is not included in figure 177?
(e) Communication with one another was an early human desire. Over the years, humans have created complex communication supply chains. What force is always present in any human communication supply chains?
(f) Demand goes to supply or supply goes to demand. Both scenarios are present amongs humans. Indicate scenarios when the former movement is preferable.
(gi) Google Search is a variant of the offload scenario. Explain.
(ii) What type of PjProblemStrings Sequence are the displayed results of a Google search?

→ Solution: the strings and the math.

Electromagnetic Waves - Invisible PjProblemStrings Sequences

Electromagnetic Waves - Invisible PjProblemsStrings

The PjProblemStrings Sequences examples given previously for each of the seven types of PjProblemStrings Sequences are visible to the unaided eyes. Some PjProblemStrings Sequences are invisible to the unaided eyes. These sequences are electromagnetic waves (excluding the visible light of the electromagnetic spectrum).

(a) How are electromagnetic waves formed?
(b) How are electromagnetic waves different from other waves (eg. ocean wave)?
(c) There are seven types of PjProblemStrings Sequences. Electromagnetic waves are PjProblemStrings Sequences. To what group will you assign them?

→ Solution: the strings and the math.

Types of PjProblemStrings Sequences

Types Of PjProblemStrings Sequences

PjProblemStrings Sequences are the work-horses of dynamic spaces. The primary types are as follows:
(1) Stand-alone PjProblemStrings Sequences
(2) Queueing PjProblemStrings Sequences
(3) Colliding PjProblemStrings Sequences
(4) Displacement PjProblemStrings Sequences
(5) Overlapping PjProblemStrings Sequences
(6) Hovering PjProblemStrings Sequences
(7) Linked PjProblemStrings Sequences

(a) Give at least one example for each of the seven types
of PjProblemStrings Sequences.
(b) Interprete Newton's first and third laws of motion in the context of PjProblemStrings Sequences.

→ Solution: the strings and the math.

The Number Line Via PjProblemStrings Sequencing

The Number Line Via PjProblemstrings Sequencing

The Number Line is a great human invention. Its current state is a consequence of centuries of development of an initial primitive one-one mapping of symbols to the existential awareness of physical quantities in space. The success of the Number Line is due to its explicit and implicit values. The myriad advanced number theories are consequences of its implicit value. The cardinality and ordinality of numbers are consequences of its explicit value.

Consider the following scenarios:
Scenario I: a crane offloads the containers of an importer from a container ship one container at a time and stores them in an allocated space onshore. The importer's guard who has the identities of the containers ensures that the containers are accurately offloaded.

Scenario II: the customers of a service company queue up in front of a service counter. The company's guard ensures an orderly queue.

(a) Which of the scenarios involves PjProblemStrings Sequencing?

(bi) Which scenario emphasizes the cardinality of numbers?
(ii) Which scenario emphasizes the ordinality of numbers?
(iii) Explain how the guards' responsibilities are influenced by
the cardinality and ordinality of the scenarios.

(c) Consider a number line initialized via PjProblemStrings Sequencing:
(i) define the 0 (zero) of such a number line.
(ii) Interprete the positive whole numbers of such a number line.
(iii) Interprete the negative whole numbers of such a number line.

(d) The coordinates of the cartesian point A(x, y, z) is derived
via PjProblemStrings Sequencing. Explain.

→ Solution: the strings and the math.