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On the Global Regularity of the 3D Incompressible Navier–Stokes Equations: A Four-Pillar Conditional Framework and Regularity Elevation Michael Allan A. Bahtaji, Ph.D. Department of Physics, Col…

On the Global Regularity of the 3D Incompressible Navier–Stokes Equations: A Four-Pillar Conditional Framework and Regularity Elevation Michael Allan A. Bahtaji, Ph.D. Department of Physics, College of Science Technological University of the Philippines Ayala Boulevard, Ermita, Manila, Philippines, 1000 Email: michaelallan_bahtaji@tup.edu.ph | michaelallanbahtaji336@gmail.com Abstract We establish a rigorous, self-contained mathematical framework addressing the global existence and smoothness of solutions to the three-dimensional incompressible Navier–Stokes equations. The formulation is structured around four technical pillars: (1)  Sobolev energy estimates () and local energy inequalities for suitable weak solutions; (2) Littlewood–Paley dyadic frequency analysis and the Beale–Kato–Majda (BKM) logarithmic criterion governing the non-linear vortex stretching operator; (3) critical scaling invariance () and anomalous energy dissipation bounds in the zero-viscosity limit (); and (4) the Caffarelli–Kohn–Nirenberg (CKN) -regularity theory establishing that the space-time singular set  has 1D Hausdorff measure zero (). We demonstrate how elevating a Leray–Hopf weak solution to a global  smooth solution reduces strictly to proving high-frequency energy decay across Littlewood–Paley blocks. Finally, we explicitly isolate the three open Millennium-level barriers that must be surpassed for an unconditional proof.

Tadqiqotda turbulеnt oqimlarning asosiy tushunchalari va fizik-matеmatik xossalari tahlil qilinadi. Turbulеntlik hodisasi laminar oqimdan farqli ravishda bеqaror, notеkis va еnеrgiyaga boy bo‘lg…

Tadqiqotda turbulеnt oqimlarning asosiy tushunchalari va fizik-matеmatik xossalari tahlil qilinadi. Turbulеntlik hodisasi laminar oqimdan farqli ravishda bеqaror, notеkis va еnеrgiyaga boy bo‘lgan harakat shaklini ifodalaydi. Tadqiqotda Rеynolds soni, еnеrgiya spеktri, impuls almashinuvi, shuningdеk, turbulеnt diffuziya va yopishqoqlik kabi paramеtrlarning roli ko‘rib chiqiladi. Turbulеnt oqimlarning strukturasi, ulardagi uyurmalar (vortеxlar) dinamikasi va ularning oqim barqarorligiga ta’siri nazariy va amaliy nuqtai nazardan o‘rganiladi. Shuningdеk, turbulеntlikni modеllashtirish usullari – statistik yondashuvlar, Navе-Stoks tеnglamalari asosidagi yondashuvlar va hisoblash suyuqliklar dinamikasi (CFD) vositalari tahlil qilinadi.

This deliverable outlines the Plan for Dissemination and Communication Activities (D5.2) for the TorPropel project, a Horizon Europe Pathfinder Open initiative dedicated to the development and demonst…

This deliverable outlines the Plan for Dissemination and Communication Activities (D5.2) for the TorPropel project, a Horizon Europe Pathfinder Open initiative dedicated to the development and demonstration of toroidal propeller technologies for sustainable and high-performance aviation.The aim of this deliverable is to define a comprehensive, strategic, and measurable plan to ensure that the project’s scientific and technological innovations are effectively communicated to relevant stakeholders and that its societal and environmental benefits are widely disseminated.

Mazkur tezisda badiiy matnlarning filolog talabalarning lingvomadaniy kompetensiyasini rivojlantirishdagi lingvodidaktik imkoniyatlari ingliz tili misolida yoritiladi. Tadqiqotning dolzarbligi zamonav…

Mazkur tezisda badiiy matnlarning filolog talabalarning lingvomadaniy kompetensiyasini rivojlantirishdagi lingvodidaktik imkoniyatlari ingliz tili misolida yoritiladi. Tadqiqotning dolzarbligi zamonaviy xorijiy til ta’limida filolog talabaning nafaqat til birliklarini bilishi, balki ularning ortida mavjud madaniy mazmunni anglash, badiiy matnni lingvomadaniy jihatdan interpretatsiya qilish, turli madaniy hodisalarni qiyoslash va o‘zlashtirilgan bilimlarni kommunikativ vaziyatlarda qo‘llash zarurati bilan belgilanadi. Badiiy matn til, madaniyat va inson tajribasini birlashtiruvchi murakkab lingvodidaktik resurs sifatida realiyalar, frazeologizmlar, metaforalar, ramzlar, antroponimlar, toponimlar, tarixiy va madaniy referensiyalar, mifologik obrazlar hamda madaniy konseptlarni o‘zida mujassamlashtiradi. Tezisda mazkur birliklarning ta’limiy imkoniyatlari, badiiy matnning interpretativ va qiyosiy salohiyati hamda filolog talabalarning lingvomadaniy kompetensiyasini rivojlantirishga yo‘naltirilgan metodik faoliyat yo‘nalishlari tahlil qilinadi.

Teacher professionalism, reflected in ethical conduct, instructional delivery, punctuality and adherence to professional standards, underpins the quality of schooling, and in Kenya the Teachers Servic…

Teacher professionalism, reflected in ethical conduct, instructional delivery, punctuality and adherence to professional standards, underpins the quality of schooling, and in Kenya the Teachers Service Commission’s Teacher Performance Appraisal and Development (TPAD) tool, introduced in 2016, is the employer’s main instrument for strengthening it. This article reports how five TPAD components, namely self-appraisal, lesson observation, continuous professional development (CPD) linked to identified gaps, feedback and performance target setting, relate to teacher professionalism in public junior schools in Tana Delta. The study was anchored on Locke and Latham’s Goal Setting Theory and used a convergent mixed methods design. Fourteen of the 45 public junior schools were sampled by proportionate stratified random sampling and 40 of 265 teachers were selected. Of these, 39 teachers returned questionnaires (Cronbach’s alpha = 0.925), 12 institutional administrators, 10 deputies and the Sub-County Director were interviewed, and lesson observations were conducted in the 14 schools using a structured schedule. Quantitative data were analyzed in SPSS Version 27 using descriptive statistics and regression at the 0.05 level of significance; qualitative data were analyzed thematically. Teachers agreed that CPD (4.36 to 4.49) and performance target setting (4.26 to 4.49) strengthen their professionalism, and were more divided on self-appraisal (3.15 to 4.56) and lesson observation (3.51 to 4.41). CPD linked to identified gaps had the strongest relationship with professionalism (R² = .777), followed by performance target setting (.721), feedback (.663), lesson observation (.595) and self-appraisal (.396). Observed lessons averaged 75.4% of the maximum score and were weakest on the use of teaching and learning resources (61.1%). The administrators reported inflated self-appraisal scores, feedback that was mostly informal, observations not logged on the TPAD portal, and inadequate ICT infrastructure. The study concludes that TPAD is positively associated with teacher professionalism in these schools, with the strongest contribution coming from gap-targeted CPD and target setting, while self-appraisal, feedback and lesson observation depend on the quality of implementation. It recommended that , the Teachers Service Commission and institutional  administrators should standardize self appraisal and feedback practices, improve lesson observation guidelines and  address infrastructural constraints such as unreliable internet connectivity and inadequate ICT facilities in order to strengthen TPAD implementation in Tana Delta Sub County and similar ASAL areas.    Keywords: Teacher Performance; Appraisal Development; TPAD; Teacher Professionalism; Continuous Professional development

This dataset provides the complete corpus of Dionisio Capuano’s “Mission: It’s Possible” column, published in the Italian music magazine Blow Up between February 2005 and Decem…

This dataset provides the complete corpus of Dionisio Capuano’s “Mission: It’s Possible” column, published in the Italian music magazine Blow Up between February 2005 and December 2011 (issues 81-163). The column was devoted to reviews of imaginary records: fictional phonographic releases attributed, in almost all cases, to actually existing artists and presented through the discursive conventions of music criticism. The corpus comprises 74 published instalments. Issues 131 (April 2009) and 157 (June 2011) are not documentary gaps: the “Mission: It’s Possible” column did not appear in those two issues. The TXT file contains the complete corpus in its original Italian, including the notes accompanying the individual instalments. Editorial information, corpus metadata and documentation supplied for this edition are in English. The XLSX file provides a structured overview of the corpus, including stable corpus IDs (MIP001-MIP074), issue numbers and dates, artists/projects, imaginary record titles, transcription sources, word counts, and analytical metadata used for corpus-level research. Instalments from issues 81-119 were transcribed from a PDF with selectable text; later instalments were reconstructed from photographs of the original magazine pages. Manifest OCR and typographical artefacts have been normalised, while doubtful readings have not been conjecturally rewritten. The corpus contains approximately 75,989 words, including the original notes and excluding editorial metadata. The dataset was prepared and edited by Gabriele Marino for research on uphonic criticism, potential discography, music criticism and quantitative semiotics.

Abstract This paper assessed the distribution of quality index of groundwater around selected waste dumpsites in Rivers State. Three waste dumpsites in Aluu, Eneka and Trans-amadi communities in River…

Abstract This paper assessed the distribution of quality index of groundwater around selected waste dumpsites in Rivers State. Three waste dumpsites in Aluu, Eneka and Trans-amadi communities in River state were randomly sampled. Groundwater sourced from boreholes sited at distances of 100m, 150m and 200m away from the dumpsites were sampled for the study in November and analyzed in laboratory for some water quality parameters (physicochemical properties are pH, BOD, COD, TDS, EC and Turbidity, while heavy metals are Copper, Nickel, Lead, Cadmium, Chromium, Iron and Zinc). The results of the analysis revealed that; some of the selected water quality parameters were within the accepted WHO standards in the three communities while some parameters are not within accepted standards especially Lead which is higher than accepted standard at 100m and 150m away from the waste dumpsite in the three communities, Water quality index (WQI = 0.87) for water sample obtained at distances of 100m away from the waste dumpsite in Aluu was not good for drinking, while WQI of 0.71 and 0.63 for sample obtain at 150 and 200m respectively were poor, therefore, need minor treatment before drinking , WQI for water sampled from Eneka at distances of 100m and 150m away from dumpsite were not for drinking (WQI = 1.05 and 0.87) while the water sampled from 2000m was  good for drinking (WQI = 0.46) while for Trans-amadi, the water sampled at distances of 100m and 150m are not good for drinking (WQI = 1.01 and 0.96) while water sampled  at 200m is poor therefore, need minor treatment before drinking (WQI = 0.73).. It was concluded that groundwater system close to waste dumpsites in Rivers State are polluted. Keywords: Water Quality Index, Groundwater, Waste Dumpsites, Rivers State

Mazkur maqolada o‘zbek va xitoy bolalar prozasida milliy tarbiya va an’analar konsepsiyasining badiiy ifodasi qiyosiy-tipologik hamda lingvomadaniy nuqtayi nazardan tadqiq etiladi. Tadqiqo…

Mazkur maqolada o‘zbek va xitoy bolalar prozasida milliy tarbiya va an’analar konsepsiyasining badiiy ifodasi qiyosiy-tipologik hamda lingvomadaniy nuqtayi nazardan tadqiq etiladi. Tadqiqot uchun o‘zbek bolalar adabiyotidan Xudoyberdi To‘xtaboyevning «Sariq devni minib» romani va G‘afur G‘ulomning «Shum bola» qissasi, xitoy bolalar adabiyotidan esa Ye Shengtaoning (叶圣陶) «稻草人» (Dàocǎorén), Bing Sinning (冰心) «小桔灯» (Xiǎo jú dēng) hamda Zhang Tianyining (张天翼) «大林和小林» (Dàlín hé Xiǎolín) asarlari tanlab olindi. Asarlardagi oila, ota-ona va farzand munosabatlari, mehnatsevarlik, bilim, halollik, insonparvarlik, umid, ijtimoiy mas’uliyat va milliy o‘zlik kabi tarbiyaviy konseptlar qiyoslanadi. Tahlil davomida bir xil umuminsoniy qadriyatlarning turli tarixiy-madaniy muhitlarda turlicha badiiy modellashtirilishi aniqlanadi. Xitoy tilidagi 孝 (xiào), 家庭 (jiātíng), 勤劳 (qínláo), 祖国 (zǔguó) kabi konseptlar o‘zbek tilidagi ota-onaga hurmat, oila, mehnatsevarlik va Vatan tushunchalari bilan qiyoslanadi. Maqolada asarlardagi konkret syujet epizodlari asosida tarbiyaviy g‘oyaning obraz, predmet, harakat va badiiy detal orqali berilishi ko‘rsatiladi.