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Bul maqalada mektep ádebiyat sabaqlıqlarında qaraqalpaq xalıq erteklerin oqıtıwdıń materiallı ‒ súwretli ‒ simvollı jantasıwlarǵa tiykarlanǵan innovaciyalıq metodologiyası izertlenedi. T…

Bul maqalada mektep ádebiyat sabaqlıqlarında qaraqalpaq xalıq erteklerin oqıtıwdıń materiallı ‒ súwretli ‒ simvollı jantasıwlarǵa tiykarlanǵan innovaciyalıq metodologiyası izertlenedi. Tiykarǵı tekst materialları sıpatında «Aqquwbay patsha», «Úsh aǵalı-inili batırlar» hám «Úsh aǵayınlı kózi ashıqlar» ertekleri alınǵan. Maqala kognitiv psixologiya, semiotika hám konstruktivlik oqıtıw teoriyalarına tayanǵan halda, xalıq awızeki dóretpelerindegi pedagogikalıq hám filosofiyalıq mazmundı oqıwshılarga úyretiwdiń nátiyjeli jolların ashıp beredi

Макалада өзбек тилдүү мектептерде кыргыз адабиятын өзбек адабияты менен байланыштырып жана салыштырып окутуунун илимий-методикалык негиздери, дидактикалык талаптары жана негизги принциптери изилденген…

Макалада өзбек тилдүү мектептерде кыргыз адабиятын өзбек адабияты менен байланыштырып жана салыштырып окутуунун илимий-методикалык негиздери, дидактикалык талаптары жана негизги принциптери изилденген. Тили жана маданияты тектеш калктардын адабий чыгармаларын салыштыруу аркылуу окуучулардын көркөм-аналитикалык ой жүгүртүүсүн, кеп маданиятын өстүрүү жана этномаданий тарбия берүү маселелери талдоого алынат. Изилдөөдө ата мекендик жана чет элдик окумуштуу-методисттердин эмгектерине таянуу менен, окутуунун заманбап усулдук принциптери, анын ичинде жасалма интеллектти методикалык колдоо мүмкүнчүлүктөрү системалаштырылып сунушталган.

A Definitive Proof of the Collatz Conjecture using the Halemane(3X±1)/4System     © Dr.(Prof.) Keshava Prasad Halemane, Professor - retired (2017JAN31) from Department of Mathem…

A Definitive Proof of the Collatz Conjecture using the Halemane(3X±1)/4System     © Dr.(Prof.) Keshava Prasad Halemane, Professor - retired (2017JAN31) from Department of Mathematical And Computational Sciences, National Institute of Technology Karnataka Surathkal, Srinivasnagar, Mangaluru - 575025, India. https://orcid.org/0000-0003-3483-3521 Independent Researcher @ SASHESHA (no affiliations; no funding; no data used; no conflict of interests) https://www.linkedin.com/in/keshavaprasadahalemane/ k.prasad.h@gmail.com     Abstract   Halemane(3X±1)/4System is defined, similar to the Collatz (3x+1) System, with slightly modified operations.  On similar lines, we define the CTUHSK(3x+1)/4System, and show that to be exactly the same as the Collatz (3x+1) System.  The convergence of Halemane(3X±1)/4System to its trivial-cycle {(1⇐(2)⇐4)} is established using the persistent local characteristic property of ‘odd-to-odd monotonicity’ in its defining function.  A reversible (invertible) transformation; between Halemane(3X±1)/4System and the CTUHSK(3x+1)/4System; based on a pruning-&-joining operation on the system arborescence; is designed, that does not affect the binary(inward)arborescence structure as well as the convergence characteristics of either of the systems.  This establishes the convergence of the CTUHSK(3x+1)/4System to its trivial-cycle {(1⇐2⇐4)}; and therefore provides a definitive proof of the convergence of the Collatz-Thwaites-Ulam-Hasse-Syracuse-Kakutani (CTUHSK) Sequence; asserting the Collatz Conjecture.   This paper also presents Halemane-Conjecture associated with the Collatz sequence, that the upper bound on the number of odd (3x+1) operations required to reach the trivial-cycle {(1⇐2⇐4)} starting from any given positive integer and moving along the Collatz sequence, is the given number itself; the triad {(31⇐41⇐27)} being an exceptional limiting case.     Keywords: Halemane(3X±1)/4System; CTUHSK(3x+1)/4System;          Halemane’s Conjecture on the Collatz (3x+1) System;          Collatz-Thwaites-Ulam-Hasse-Syracuse-Kakutani (CTUHSK) Sequence;          Collatz-Thwaites-Ulam-Hasse-Syracuse-Kakutani (CTUHSK) Conjecture;          binary(inward)arborescence;     AMS MSC Mathematics Subject Classification:  11B83; 11Y55; 40A99; 93A99.   Summary   Halemane(3X±1)/4System has been defined, similar to the Collatz (3x+1) System; with slightly modified operations.  We have also defined the CTUHSK(3x+1)/4System, and shown that to be exactly the same as the Collatz (3x+1) System.  The global convergence of Halemane(3X±1)/4System to its trivial-cycle {(1⇐(2)⇐4)} is established through the local monotonicity property of the defining function.  A reversible (invertible) transformation between Halemane(3X±1)/4System and CTUHSK(3x+1)/4System has been designed, based on a process consisting of pruning-&-joining operations performed recursively/iteratively on the binary(inward)arborescence structure of the system.  This pruning-&-joining operation does not affect the binary(inward)arborescence structure as well as the convergence characteristics of either of the systems, because the pruned subtree is joined onto an already existing inactive-node of the system arborescence.  Therefore, this establishes the convergence of the Collatz-Thwaites-Ulam-Hasse-Syracuse-Kakutani (CTUHSK) Sequence and providing a definitive proof of Collatz Conjecture.   Halemane-Conjecture on the Collatz (3x+1) sequence states that the maximum limit on number of odd (3x+1) operations required to reach the trivial-cycle {(1⇐2⇐4)}; starting from any given positive integer and moving along the Collatz sequence; is the given number itself; with the triad {(31⇐41⇐27)} as an exceptional limiting case.    

A skill tree is a graph of the skills and concepts in one school subject, written by a teacher, with an instruction on each node that a student copies into an AI chat. This repository holds the render…

A skill tree is a graph of the skills and concepts in one school subject, written by a teacher, with an instruction on each node that a student copies into an AI chat. This repository holds the rendering engine, the instructions, the interface languages and the decomposition model.

Бул макалада дүйнөлүк илимде жана технологияда инновациянын генезиси, анын ар түрдүү тармактарда пайда болушу тууралуу айтылат. Автор жалпы педагогикадагы инновация түшүнүгүн талдоого алып, педагогика…

Бул макалада дүйнөлүк илимде жана технологияда инновациянын генезиси, анын ар түрдүү тармактарда пайда болушу тууралуу айтылат. Автор жалпы педагогикадагы инновация түшүнүгүн талдоого алып, педагогикалык инновациялардын көп жактуулугуна токтолгон.

Background: Digital technologies have disrupted traditional journalistic verification, creating an ecosystem where speed increasingly supersedes accuracy. A gap remains in understanding how edito…

Background: Digital technologies have disrupted traditional journalistic verification, creating an ecosystem where speed increasingly supersedes accuracy. A gap remains in understanding how editors negotiate these competing imperatives, especially in developing systems like Nigeria. Objective: This study examined how the demand for immediacy influences journalistic judgment, verification routines, and credibility in Nigeria's digital media environment. Method: Using a qualitative descriptive design, semi-structured interviews were conducted with six purposively selected Nigerian legacy and online newspaper editors based in Lagos, Nigeria. Data were analysed using thematic analysis. Results: The speed-accuracy paradox compromises verification and weakens gatekeeping. Algorithms act as "shadow editors," prioritising virality and commercial survival over factual depth. A gap exists between awareness of digital verification tools and operational proficiency, leading editors to rely on traditional, human-centric methods. This speed-oriented culture erodes professional ethics and identity. Conclusion: The accuracy-first mandate remains a non-negotiable requirement for journalistic survival. Operating with a "publish now, correct later" mentality compromises journalism's social contract, making it indistinguishable from digital noise. Unique Contribution: The study integrates Speed-Accuracy Tradeoff and Gatekeeping theories to demonstrate that verification failures are institutional and structural, not just individual lapses. Key Recommendation: Media houses must transition from tool awareness to operational proficiency, establish independent quality assurance firewalls, and prioritise factual sovereignty over chronological dominance.

What's Changed Close roadmap §1.1 and §1.2: deck writers, read-only reasons, shared node orders (v16.17.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/112 Roadmap §4: te…

What's Changed Close roadmap §1.1 and §1.2: deck writers, read-only reasons, shared node orders (v16.17.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/112 Roadmap §4: text reading and raw appended VTU (v16.20.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/113 Roadmap §4: I/O (v16.19.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/111 Roadmap §4: the rest of the operation items (v16.18.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/110 Roadmap §4: operations, I/O, text reading and raw appended VTU (v16.18.0–v16.21.0) by @loumalouomega in https://github.com/loumalouomega/meshioplusplus/pull/109 Full Changelog: https://github.com/loumalouomega/meshioplusplus/compare/v16.16.0...v16.21.0

Ushbu maqolada milliy urf-odat, qadriyat va an’analarning yosh avlod tarbiyasidagi o‘rni va ahamiyati yoritilgan. Milliy qadriyatlar xalqning ko‘p asrlik hayotiy tajribasi, ma’…

Ushbu maqolada milliy urf-odat, qadriyat va an’analarning yosh avlod tarbiyasidagi o‘rni va ahamiyati yoritilgan. Milliy qadriyatlar xalqning ko‘p asrlik hayotiy tajribasi, ma’naviy dunyoqarashi va axloqiy mezonlarini o‘zida mujassam etishi, ularni yoshlar ongiga singdirish orqali vatanparvarlik, insonparvarlik, kattalarga hurmat, kichiklarga izzat, mehr-oqibat va mas’uliyat kabi fazilatlarni shakllantirish mumkinligi tahlil qilingan.

Maqolada XX asr boshlaridagi o‘zbek nasrida ijtimoiy muhit va inson taqdiri masalasi badiiy talqin nuqtai nazaridan yoritilgan. Unda A.Qodiriyning “Mehrobdan chayon”idagi Nazmi, G&ls…

Maqolada XX asr boshlaridagi o‘zbek nasrida ijtimoiy muhit va inson taqdiri masalasi badiiy talqin nuqtai nazaridan yoritilgan. Unda A.Qodiriyning “Mehrobdan chayon”idagi Nazmi, G‘.G‘ulomning ”Netay” qissasidagi Netay hamda Cho‘lponning “Kecha va kunduz” romanidagi Zebi timsollari qiyosiy tahlil qilinadi. Qahramonlar fojiasi orqali davrning ijtimoiy illatlari va ayollar huquqsizligi muammosi ochib beriladi