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Integrated Taxonomy of Materials with Industry Standards 1. Metals and Alloys Classification Standards: ISO 4948: Classification of metallic materials ASTM Axxx / Bxxx / Exxx: Material-specific standards UNS (Unified Numbering System): e.g., AISI 304 = UNS S30400 Subtypes: Class Example Standards Ferrous Steel, Cast Iron ISO 4948, ASTM A36, UNS G10200 Non-ferrous Copper, Aluminum ASTM B209, ISO 6361, UNS A91100 2. Polymers Classification Standards: ISO 1043: Codes for polym...

Hierarchical Structure of Electrical and Electronics Engineering Materials 1. Classification by Function 1.1 Conductive Materials Copper Aluminum Silver Gold Graphene 1.2 Resistive Materials Manganin Nichrome Carbon composition Tantalum nitride 1.3 Insulating (Dielectric) Materials PVC Bakelite Teflon Glass Mica Ceramic 1.4 Semiconducting Materials Silicon (Si) Germanium (Ge) Gallium arsenide (GaAs) Silicon carbide (SiC) Indium phosphide (InP) 1.5 Magnetic Materials Soft Magne...

Parent Fields for Category Theory Category Theory is a high-level mathematical framework that generalizes various mathematical structures. It draws on several parent disciplines. Below is an expanded breakdown of the parent fields that contributed to the development and understanding of Category Theory. 1. Abstract Algebra Subfields: Group theory Ring theory Module theory Lattice theory Contribution: Morphisms and homomorphisms: The notion of structure-preserving maps originates here....

Category Theory Symbols with Examples 1. Objects and Morphisms Symbol Name Meaning Example A, B, C Objects Abstract elements in a category A, B ∈ Ob(C) f, g Morphisms Arrows between objects f: A → B idₐ Identity Identity morphism on A idₐ: A → A ∘ Composition Compose morphisms g ∘ f: A → C (if f: A→B, g: B→C) 2. Categories and Collections Symbol Name Meaning Example 𝒞, 𝒟, 𝐄 Category names Categories are collections of morphisms 𝒞 = Set, 𝒟 = Grp Ob(𝒞) Objects Set of ob...

Logic Symbols with Examples 1. Propositional Logic Symbol Name Meaning Example ¬ Negation Not ¬P: Not P ∧ Conjunction And P ∧ Q: P and Q ∨ Disjunction Or P ∨ Q: P or Q ⊕ Exclusive Or Either but not both P ⊕ Q: P or Q, but not both → Implication If..., then... P → Q: If P, then Q ⇐ Converse Q if P Q ⇐ P: Q if P ⇔ Biconditional If and only if P ⇔ Q: P if and only if Q ⊤ Tautology Always true P ∨ ¬P: tautology ⊥ Contradiction Always false P ∧ ¬P: contradiction 2. Predi...

Signs Used in Set Theory 1. Membership and Non-Membership Sign Name Meaning ∈ Element of x ∈ A: x is an element of A ∉ Not an element of x ∉ A: x is not an element of A 2. Set Inclusion and Equality Sign Name Meaning ⊆ Subset A ⊆ B: A is a subset of B ⊂ Proper subset A ⊂ B: A is a proper subset of B ⊇ Superset A ⊇ B: A is a superset of B ⊃ Proper superset A ⊃ B: A properly contains B = Equality A = B: A and B are equal ≠ Inequality A ≠ B: A and B are not equal ...

Phoneme = Phonology Phone = Phonetics Phoneme types included: Consonants Vowels Suprasegmentals (tone, nasalization, etc.) No allophones; only distinct phonemes Visualize(frequency of phonemes) Open and downloadable in CSV/JSON formats Integrated: PHOIBLE (Phonetics Information Base and Lexicon) expands on UPSID https://phoible.org Data Sources: UPSID (UCLA Phonological Segment Inventory Database) UPSID (UCLA) WALS (World Atlas of Language Structures) PHONDATA LAPSYD Other fi...

Types of Ciphers with Examples 1. Monoalphabetic Substitution Cipher Each letter maps to another single fixed letter. Plaintext: HELLO Cipher Key: A→M, B→N, C→O, ..., H→T, E→Q, L→X, O→Z Ciphertext: TQXXZ 2. Caesar Cipher (Shift Cipher) Each letter is shifted by a fixed number. Shift: +3 Plaintext: ATTACK Ciphertext: DWWDFN 3. Atbash Cipher Reverses the alphabet. A ↔ Z, B ↔ Y, ..., M ↔ N Plaintext: HELLO Ciphertext: SVOOL 4. Keyword Cipher Uses a keyword to reorder th...

மொழி முதல் இடை இறுதி எழுத்துகள் ஒவ்வொரு இடத்திலும் மொத்தம் 247 அல்லது 31 அல்லது 30 மொத்த நிகழ்வுகள் தற்போது உள்ளன. _ ஓரெழுத்தொருமொழி - ஈரெழுத்தொருமொழி --மூவெழுத்துச் சொற்கள் _--- ... நான்கு அதற்கு மேற்பட்ட எழுத்துருக்கள் கொண்ட சொற்கள் வருபவை 22->30->(23+1) வராத வை 8->0->7+1 இவற்றின்படி: தமிழைப் பிழையின்றி எழுதுவோம், 11ம் வகுப்பு தமிழ், இலக்கண வரைபடங்கள், 6 வது தமிழ். முதல்: வந்த/வருப 103/247 அ 22/30 வராத 144/247 அ 8/30 இடை: வந்த/வருப மெய், உயிர்மெய், ஆய்தம், அளபெடை 235/...

Root Nouns – Concept Tree 1. Semantic Role Abstract nouns – e.g., freedom, idea, courage Proper nouns – e.g., Einstein, India, Jupiter Collective nouns – e.g., team, flock, committee Mass nouns – e.g., water, rice, information Event nouns – e.g., birth, explosion, ceremony State nouns – e.g., condition, balance, awareness Agent nouns – performer of action (e.g., teacher) Patient nouns – receiver of action (e.g., victim) 2. Ontological Category Physical entities – e.g., stone, table Proces...

Referent Variant Functions and Relations 1. Core Terminology Referent: The actual entity or object in the world that a linguistic or symbolic expression refers to. Reference: The act of pointing to or denoting a referent from within a system (e.g., language, logic, model). Variant: A change in form, role, or relation of the referent depending on context, function, or observer. 2. Function Types A. Constant Reference Functions Definition: A function where the output (referent) does not ...

Observation is Relative – Structured by Standard Terminology 1. Epistemology (Philosophy of Knowledge) Subject (epistemic agent): A self-aware entity capable of cognition, perception, and intentionality. Object (epistemic content): That which is known, perceived, or thought about by the subject. Subject–Object Relation: A directed relation where knowledge flows from subject → object. Principle: The same entity may act as subject or object, depending on who observes whom. 2. Phenomenolo...

Observer vs Object – A Cross-Domain Conceptual Link 1. Grammatical Domain Term Role Notes I First person Always subject You Second person Subject or object He/She/It Third person Can be subject or object Link: Grammatical subject ≠ philosophical subject necessarily. 2. Logic & Set Theory Concept Meaning Subject The entity that asserts, observes, or acts Object The entity that is asserted about Relation A mapping from subject to object Domain Set of possible subje...

Atomic Concepts of Knowledge Systems Definition Atomic concepts are the smallest indivisible units of meaning or knowledge that cannot be broken down further within a given system. They serve as the building blocks for all complex ideas, theories, and formal systems. Purpose Foundation: Provide a minimal set of core elements for knowledge representation. Composability: Combine to form higher-level concepts or compound structures. Universality: Enable cross-domain integration through share...

Characteristica Universalis – Leibniz's Vision of a Universal Language Definition Characteristica Universalis (Latin for "universal character") is a formal symbolic language proposed by Gottfried Wilhelm Leibniz to represent all human knowledge in a precise, logical, and calculable form. "Let us calculate." — Leibniz Components Term Meaning Characteristica A system of formal, symbolic notation Universalis Intended to be universal across all domains of human knowledge Calculus R...

Intersection – Conceptual Overlaps Across Domains Universal Pattern Intersection = Common part of two or more sets, concepts, or structures The intersection is the shared element(s) among multiple domains, entities, or states. It identifies what is mutual, overlapping, or co-existing. Mathematics & Logic Set Theory Intersection (A ∩ B): Elements common to both sets A and B. Logic Logical AND (P ∧ Q): True only when both P and Q are true. Boolean Algebra AND Operation: Bi...

Another from Whole – Conceptual Complements Across Domains Universal Pattern Complement = Whole – Part The complement is what remains when a part is removed from a whole. It applies across logic, math, language, and systems. Mathematics & Logic Set Theory Complement (Aᶜ): Elements in the universal set U that are not in A. Logic Negation (¬P): The opposite truth value of proposition P. Boolean Algebra Complement (A'): Bitwise NOT; inverts each bit or truth value. Number...

Tree Summary (Hierarchy) Leibniz's Works ├── Characteristica Universalis (Universal Language) │ └── Symbolic representation of all knowledge ├── Calculus Ratiocinator (Logical Calculus) │ └── Symbolic manipulation of reasoning ├── Binary Logic (0 and 1) │ ├── Arithmetic foundation │ └── Logic encoding (true/false) ├── Philosophical Logic │ ├── Principle of Sufficient Reason │ ├── Identity of Indiscernibles │ └── Pre-established Harmony └── Influence Tree ├── Boolean Algebra ...

Comparative Overview: Venn Diagrams, De Morgan’s Rules, Logical Operators, Set Theory, Boolean Algebra, Leibniz’s Works 1. Overview Table Concept Domain Core Function Historical Context / Originator Venn Diagram Visual Logic / Set Theory Shows set relations using diagrams John Venn (1880) De Morgan’s Rules Logic & Set Theory Negation distribution laws for AND/OR or ∩/∪ Augustus De Morgan (1847) Logical Operators Propositional Logic Symbols for combining truth-values Frege, Boole...

Comparison: Logical Operators vs. Set Theory Symbols 1. Functional Purpose Category Purpose Logical Operators Manipulate truth values of propositions (T/F logic) Set Theory Symbols Describe relationships between sets and elements 2. Symbol Comparisons (Similar Meaning, Different Domain) Logic Symbol Set Theory Symbol Logic Meaning Set Theory Meaning ∧ (AND) ∩ (Intersection) A and B are both true Elements common to sets A and B ∨ (OR) ∪ (Union) At least one of A or B is true...

Trigraph Focus: "tra" and "sta" This document outlines linguistic, phonological, morphological, and lexical details about the trigraphs "tra" and "sta" in English. 1. Overview Trigraph Position Common Function Origin tra Initial Lexical stem/root prefix Latin, Greek sta Initial Lexical stem/root prefix Latin 2. Graphemic Frequency Trigraph Approximate Frequency Rank (Among Trigraphs) tra Moderate Top 200 sta Moderate–High Top 150 Sources: COCA, Google Ngram, SUBTLEX ...

Grapheme Frequency in English Words This document outlines the frequency of graphemes (letters and letter combinations) in English text. Graphemes can be single letters, digraphs (2 letters), trigraphs (3 letters), or tetragraphs (4 letters), often representing single phonemes or spelling patterns. 1. Single-Letter Frequencies Grapheme Frequency (%) Example Words E 12.7 bed, feel, end T 9.1 top, start, late A 8.2 cat, table, glass O 7.5 go, stop, doll I 7.0 in, time, slim N 6...

Tagmemic Hierarchy: Function + Class Across Levels In Tagmemic theory, a tagmeme is the smallest functional unit of grammar, defined by a pairing of: Function (the slot/role) Class (the phrase, clause, or unit that fills it) This structure scales across levels: phrase, clause, and discourse. 1. Phrase-Level Tagmemes Syntactic Function Phrase Type (Class) Tagmeme Example Sentence Subject Noun Phrase (NP) Subject–NP [The cat] sleeps. Predicate Verb Phrase (VP) Predicate–VP The cat ...

Tagmemes: Function + Phrase Type (Class) In Tagmemic theory, a tagmeme is defined as a pairing of a syntactic function (slot) and the phrase class (filler) that occupies it. Table of Common Tagmemes Syntactic Function Phrase Type (Class) Tagmeme Example Sentence Subject Noun Phrase (NP) Subject–NP [The cat] sleeps. Predicate Verb Phrase (VP) Predicate–VP The cat [sleeps quietly]. Object Noun Phrase (NP) Object–NP She found [the keys]. Complement Adjective Phrase (AdjP) Complement...

Visual Tree Atomic Units (-on) ├── Linguistic Units │ ├── Morpheon → morphological structure (rare) │ ├── Lexon → lexical relation (ontology-specific) │ └── Glosson → sign unit (Hjelmslev, historical) ├── Phonetic / Acoustic Units │ └── Phonon → metaphorical sound unit (rare usage in linguistics) ├── Semantic / Cognitive Units │ ├── Semion → unit of meaning (semiotics, rare) │ ├── Noeton → unit of thought (philoso...

Semantic Units (-semes) ├── Core Semantics │ ├── Sememe │ ├── Pleseme │ └── Episeme ├── Cognitive Semantics │ ├── Nooseme │ └── Lexiseme ├── Pragmatics │ └── Pragmatoseme └── Semiotic Structures ├── Narratoseme └── Mythoseme ...

Here is a semantic taxonomy tree in .md format, organizing all known and proposed -seme terms by field: Taxonomy of -seme Units in Linguistics and Semiotics The suffix -seme indicates semantic units — building blocks of meaning, ranging from abstract features to culturally contextualized signs. I. Core Semantic Units (General Semantics) Sememe Minimal unit of meaning (like a morpheme in morphology) Pleseme A sememe carrying emotive or stylistic nuance Related to connotation or ...

Common Morphemic Suffixes in Academic and Disciplinary Terms These suffixes are used to form nouns indicating fields of study, systems, or doctrines. 1. -logy Origin: Greek logia ("the study of") Function: Forms nouns denoting the study or science of a subject Examples: Biology — study of life Neurology — study of the nervous system Linguistics → not a -logy, but same family 2. -ics Origin: Greek -ika / Latin -ica Function: Forms plural-looking singular nouns for disciplines or practi...

Sememe — Definition and Structure Sememe is the minimal unit of meaning in semantics, analogous to the morpheme in morphology. It represents the atomic semantic content conveyed by a linguistic unit. A sememe is not tied to form (sound or writing), but to abstract meaning. Properties of a Sememe Abstract: Not necessarily a word or morpheme. Semantic unit: Represents a single concept or feature. Can be componential: Combined to build complex meanings. Example The word: “Man” Can...

Tagmeme — Definition and Structure Tagmeme is a term from Functional Linguistics (especially in Pikean linguistics) representing the minimal functional unit of syntax. It unites two elements: Function — the grammatical role a slot performs (e.g., Subject, Predicate) Class — the type of grammatical element that can fill that slot (e.g., NP, VP, AdjP) Structure of a Tagmeme A tagmeme is defined as a Function-Class pairing. Example: In the sentence: The dog barked. Function Class (Fil...