Applied Mathematics and Statistics

| Zenodo Open Access | CC BY 4.0 STATUS-SPECULATIVE CONCEPT PAPER. This document is a clearly-labeled thought experiment, not a derivation and not a report of results. The mathematics in §2 is rigorous and fully proved-a set of exact results about the golden ratio and the depth-2 recursion. The physics is not: the propulsion narrative (plasma-charged tesseract geometry, macro-scale branch selection, dimensional transition) is presented as a conceptual exploration, pending a first-principles derivation that does not yet exist. No physical mechanism is derived here. Under Protocol V3.1, nothing here is confirmed; all predictions are speculative and technology-gap. Concept attribution. The interdimensional-transition concept and the "blooping out of the dimensional plane" imagery were originally conceived by Michael Creasey Jr. (@AscendedSouLz) in discussion on May 6, 2026, as a creative/speculative idea. This paper frames that idea in FCLT language; it does not claim either party has derived it.

The spatial architecture of a spun staple yarn cross-section is governed by geometric selection probabilities that are strictly proportional to individual fibre length. This article develops a comprehensive probabilistic framework for modelling cross-sectional fibre population composition through stereological length-biased sampling of fibre length distributions obtained from automated fibre individualisation and measurement systems. The central mathematical principle-that the probability of any given fibre intersecting an arbitrary transverse cutting plane is directly

The transformation of staple yarn from the ring-spinning frame to a final wound package via high-speed autoconing equipment represents one of the most consequential quality-state transitions in short-staple textile manufacturing. A well-documented and industrially significant paradox consistently emerges from this transformation: the autoconed package exhibits a markedly improved profile with respect to large, severe fault classifications, yet simultaneously presents an elevated Imperfection Index (IPI) — comprising short thick places, thin places, and neps — when subjected to objective laboratory analysis via capacitive evenness measurement technology. This apparent contradiction, wherein yarn quality simultaneously improves in macro-defect severity and deteriorates in micro-defect frequency, is not indicative of machine malfunction; rather, it is the mathematically predictable and mechanistically explicable outcome of four interacting phenomena.
The present article develops a comprehensive phenomenological and statistical framework elucidating these phenomena within the scope of this conceptual analysis. First, the excision of large fault zones by the electronic clearer platform induces a statistical redistribution effect: the removal of massive mass excursions subtly lowers the computed mean yarn mass, thereby unmasking previously sub-threshold deviations and transforming a small number of large faults into a larger population of short mass disturbances. Second, the extreme winding velocities and associated ballooning dynamics impose genuine tribological damage — generating friction-induced fibre entanglements and thin zones through abrasive unwinding mechanics. Third, every pneumatic splice joint deposited during fault clearance represents an engineered structural disturbance that registers as a transient mass anomaly in capacitive evenness testing. Fourth, the metrological sensitivity of the testing equipment to dimensional flattening and compactness variation amplifies the apparent imperfection count beyond the level attributable to genuine drafting faults alone.
The framework is further extended to examine the differential degradation behaviour of compact-spun versus conventionally ring-spun yarns under winding conditions, the influence of upstream preparatory parameters on winding vulnerability, and the strategic justification for accepting a moderately elevated IPI in the context of high-speed fabric formation requirements. Ten governing equations are formalised, six analytical figures are presented, and practical guidance for quality practitioners is derived. This article presents a theoretical framework. No experimental measurements are reported herein. All parameter values are uncalibrated and require experimental determination specific to each fibre type, yarn count, and machine configuration

We present two infinite families of APN functions on GF (2 n ) where n is divisible by 3 but not 9. Our families contain two already known families as special cases. We also discuss the inequivalence proof (by computation) which shows that these functions are new.

The ring-spinning balloon constitutes one of the most dynamically complex and commercially consequential phenomena in continuous staple fibre yarn manufacturing. This article presents a comprehensive theoretical framework encompassing the formation, morphological classification, governing equations of motion, aerodynamic behaviour, and active mechanical control of the

This article presents a comprehensive theoretical and conceptual framework for the analysis of fiber migration dynamics within staple yarn ring spinning. Fiber migration — the continuous, cyclic radial interchange of individual staple fibers along the longitudinal axis of a yarn — constitutes the foundational cohesive mechanism by which discrete, discontinuous fibers are consolidated into a load-bearing continuous structure. Without this radial interchange, staple yarn integrity would be critically compromised.
Within this theoretical framework, the study rigorously delineates the sequential stages of fiber radial displacement. Spatial segregation in the drafting zone, wherein long fibers preferentially occupy the yarn core under high frictional constraint while short fibers are displaced peripherally, is analysed through the mechanics of roller drafting. Subsequently, continuous helical migration within the spinning triangle is modelled through Morton's tension variation mechanism and Hearle and Bose's geometric ribbon-twisting model, both of which are formalised as mathematical frameworks within the scope of this analysis.
A unified normalized Migration Index is introduced, incorporating three penalty functions — the length penalty f_L, the friction penalty f_μ, and the elastic stiffness penalty f_E — each with uncalibrated empirical constants requiring experimental determination specific to fibre type and machine configuration. The theoretical influence of top arm load, total draft ratio, and break draft ratio on mass unevenness is formalised through the Law of Large Numbers and a Root-Sum-Square variance decomposition model. The study further analyses systemic differences in migration intensity across conventional ring spinning, compact spinning, and open-end rotor spinning geometries. Finally, the modulating role of relative humidity on triboelectric charge generation and inter-fiber adhesion is analysed within its bounds. The framework is intended to guide practitioners of staple yarn spinning in understanding the physical determinants of yarn cohesion, structural quality, and process stability as a basis for informed engineering decisions.

Drafting zone instability is a primary determinant of yarn quality variability in ring spinning, yet the fibre population dynamics governing this instability have lacked a unified mathematical representation capable of simultaneous treatment of multi-state fibre motion, parametric process sensitivity, and multi-zone cascade propagation. This article introduces Fibre State Matrix Mechanics (FSMM), a stochastic transition framework grounded in absorbing Markov chain theory and linear systems analysis, which models the probabilistic evolution of fibre populations across four physically motivated discrete states within the drafting zone: Controlled (C), Floating (F), Accelerating (A), and Delivered (D). The framework is formulated through a (4×4) state transition matrix T, whose row-stochastic property guarantees probability conservation, and whose fundamental matrix N = (I-Q)⁻¹ yields closed-form expressions for expected fibre residence times and variance of absorption times in each transient state. A parametric extension T(p)-in which transition probabilities are explicit functions of the process parameter vector p = [D_r, L_f, P_nip, RH]ᵀ-enables structured sensitivity analysis and provides a natural correspondence with Design-of-Experiments methodology. A force coupling matrix M formalises the simultaneous action of inter-fibre friction, aerodynamic disturbance, mechanical vibration, and electrostatic forces on floating fibres; the asymmetry of M (M ≠ Mᵀ) is interpreted as a mathematical signature of the non-conservative, dissipative character of the drafting system. Eigenvalue decomposition of T yields the proposed Drafting Stability Index (DSI = 1-λ₂/λ₁), a scalar instability measure whose variation under parametric perturbation is shown to follow the expected physical trends. Observable definitions analogous to quantum mechanical expectation values are proposed to connect the abstract state formalism to measurable yarn quality metrics, including yarn mass irregularity and end-break rate. This article presents a theoretical framework only. No experimental measurements are reported herein. All parameters described are uncalibrated; values require experimental determination specific to each fibre type and machine configuration, within the scope of this conceptual analysis.

The discipline of ring spinning — the dominant technology for the production of staple-fibre yarns worldwide — is governed at every operational stage by the laws of classical mechanics and fluid dynamics. Yet the mathematical language that underlies these laws, namely differential and integral calculus, remains largely implicit in practitioner literature, scattered across specialised treatises in textile physics rather than presented as a unified, zone-resolved framework accessible to the engineering practitioner. This article addresses that gap by developing a systematic, zone-by-zone account of how the derivative operator and the definite integral appear in, and give precise mathematical form to, the five principal physical zones of the ring-spinning system: the drafting zone, the twist-insertion zone, the yarn balloon zone, the ring–traveller interaction zone, and the package winding and end-breakage zone.
Within this theoretical framework, seventeen governing equations are derived or stated, each rigorously attributed to its physical origin and each accompanied by an explicit statement of the physical meaning of its mathematical operator. The drafting zone is analysed through the spatial derivative of fibre velocity and the mass-continuity equation, yielding a direct link between velocity gradients and yarn linear-density irregularity. Twist insertion is formalised as a definite integral of local twist rate along the yarn path, and the Euler–Eytelwein capstan equation is derived as the exponential solution of a first-order linear ODE. The yarn balloon is shown to be the solution surface of a second-order nonlinear ODE, with aerodynamic drag and tension profile recovered as definite integrals over the balloon height. Traveller tribodynamics are characterised through the second time-derivative of radial position and the time integral of frictional power dissipation. Finally, winding geometry is expressed as a polar arc-length integral, and yarn end-breakage probability is cast as the Weibull cumulative distribution function.
This article presents a theoretical framework; no experimental measurements are reported herein. All figures are theoretical and illustrative; parameter values are selected for pedagogical clarity only, and all uncalibrated parameters carry explicit calibration disclaimers. The scope is confined to conventional ring spinning of staple-fibre yarns under steady-state operating assumptions and within the parameter values stated for each zone.

By defining the limits and the design specification, that an underwater robotic vehicle should fulfill in order to be characterized as biomimetic, a shell structure with a modular locomotion mechanism is proposed, using THUNDER piezoelectric, for a novel biomimetic underwater robot.  Smart materials and especially piezoelectric actuators are an excellent alternative as a propulsion mechanism for our underwater swimming fish-like robot (SRFL swimming robot with fish-like locomotion), due to their unique characteristics. This paper presents the design characteristics, the restrictions in dimensions and weight of the underwater robot and the ability of it, for maneuverability. Furthermore, the articulated locomotion mechanism of the caudal fin is designed and analyzed, while the distribution of the pressure forces on the shell, as well as in the articulated mechanism of the tail fin is also determined. Finally, the articulated mechanism is represented in MATLAB/SIMSCAPE in order to sim...

Drafting systems in ring spinning convert rove or sliver into a finely attenuated strand through a series of roller pairs, each imposing controlled draft ratios on the fibre bundle. The mechanical performance of such systems is governed not only by draft ratio and fibre characteristics but fundamentally by the tribological interactions at the roller-fibre-surface interface. Despite extensive research on process parameters and fibre behaviour, a rigorous, multi-dimensional framework quantifying how surface geometry compatibility drives tribological outcomes has remained absent from the scholarly literature.

The mechanical drafting of staple fibre assemblies represents the most kinematically critical and theoretically least resolved operation in staple fibre spinning. Despite more than a century of empirical study and progressive machine evolution, no universal deterministic model exists that can predict the precise temporal and spatial trajectory of individual staple fibres within the dynamic drafting zone. The present work advances a rigorous theoretical examination of the multiphysics nature of fibre control, synthesising principles from discrete granular mechanics, contact tribology, stochastic dynamical systems, non-Newtonian fibre rheology, and finite element analysis into a coherent conceptual framework. Central to this framework is the formalisation of the Fibre Control Index (FCI) — a dimensionless instantaneous process metric defined as the ratio of mechanically governed fibres to the total fibre population at any given moment — proposed as a complementary, proactive in-process descriptor intended to augment, not replace, conventional post-process quality metrics such as mass unevenness coefficient of variation (CV_m%) and yarn imperfection counts (thick places, thin places, and neps). Theoretical analysis reveals that fibre control breakdown is governed by the complex and largely unresolved interaction of six physical domains: contact mechanics, dynamic friction, fibre elasticity, stochastic biological variability, inertial fluid dynamics, and triboelectric charging. The floating fibre problem — characterised as the irreversible stochastic transition from deterministic roller-controlled fibre motion to turbulent friction-matrix-dependent drift — is identified as the fundamental root-cause mechanism underpinning the complete spectrum of yarn structural defects, including thick and thin places, neps, hairiness anomalies, and catastrophic end-breakages. The avalanche effect, arising from the cascade acceleration of insufficiently restrained fibres, is modelled as a granular instability analogous to turbulent flow onset. A hybrid Discrete Element Method–Finite Element Analysis digital twin framework is proposed as the principal computational pathway to achieving real-time FCI estimation. Practical implications for process engineers operating within the boundary conditions of ring spinning, air-jet spinning, and rotor spinning systems are discussed within the scope of the theoretical framework presented herein. This work proposes the FCI as a candidate in-process metric for investigation in future spinning process control research.

This paper concentrates to use two advanced statistical methods (Box-Jenkins and Adaline Neural Network) to forecast future values using data from the past values of a variable of all people that they had taken Erbil Airport as a way to move to other countries. The real data set were collected and obtained from Erbil International Airport and The sample observation consisted of (72) month, from the Airport transfer process during a certain time period 2017-2022. For the purpose of choosing the best model fit for these two models, the values of three criteria measures Mean Square Error (MSE), Mean Absolute Deviation (MAD) and Akaike Information Criterion (AIC) have been obtained from the estimated models. Additionally, the results showed that although the parameter estimations of the two models are not directly comparable, the results of all two models are not similar. Software packages StataV.16, SPSS V.26 and Matlab (R2013a) were used to fit the models.

The transformation of a 0.60 Ne roving-recording zero Imperfections Per Kilometre (IPI) on an automated yarn mass-evenness analyser-into a 30 Ne ring-spun yarn exhibiting 30 to 40 IPI constitutes one of the most frequently misunderstood phenomena in industrial staple-fibre spinning practice. This article presents a comprehensive, mathematically rigorous analysis of the four primary mechanisms governing this behaviour: (i) the absolute mathematics of signal amplification arising from a mechanical draft of 50, wherein any relative mass defect in the roving is multiplied by the draft ratio; (ii) the countdependent architecture of imperfection thresholds in mass-evenness instrumentation, defined as fixed percentage deviations from an ever-shrinking cross-sectional mean; (iii) the statistical inevitability of mass irregularity governed by Poisson distribution theory and Martindale's theoretical limit of irregularity; and (iv) the fluid-dynamic instabilities inherent to high-draft ring spinning frames, including non-Newtonian shear thinning, floating-fibre avalanche effects, and drafting wave formation. Within the analytical framework presented, a Total IPI of 30-40 km⁻¹ for a 30 Ne yarn is demonstrated to be consistent with elite, world-class global spinning benchmarks. Spectral analysis interpretation, break-draft optimisation principles, and structured practical guidance are provided for spinning mill process engineers and quality technologists.

The Yarn Body-a statistical envelope defining the acceptable amplitude distribution of yarn faults across the fault-length axis-is conventionally treated as a visualisation and limit-setting tool. This article proposes a formal reinterpretation: the Yarn Body is the observable realisation of a latent Gaussian Process (GP) defined over fault-length space. Under this formulation, the mean function μ(l) and covariance kernel K(l, l') jointly encode the complete stochastic structure of yarn fault generation. A critical practical consequence follows: when fault counts are observed in a subset of classification channels, the GP posterior-computed analytically via the Schur complement inversion-yields optimal minimum-variance predictions for all unobserved channels, together with calibrated uncertainty bounds. This Cross-Channel Fault Inference (CCFI) framework enables prediction of cut rates, Clearing Index values, and contamination exceedance probabilities in fault classes that have not been directly measured, from partial sensor observations. The theoretical derivation is presented in full, two kernel families (squared exponential and Matérn 5/2) are analysed for appropriateness to yarn fault physics, and the connection to the existing Yarn Body, Smart Limits, and Clearing Index formalism is established. Simulated validation confirms prediction accuracy within quantified RMSE bounds. The framework provides a foundation for adaptive limit optimisation, sensor-reduced quality monitoring architectures, and physics-informed fault prognosis in ring-spinning and winding operations.

The large-scale adoption of mechanically recycled cotton (MRC) and chemically recycled polyester (rPET) into high-speed ring spinning lines represents one of the most physically demanding transitions in contemporary textile manufacturing. This investigation presents a rigorous multiphysics analysis of the structural degradation, tribological dynamics, and environmental consequences arising from high-volume recycled fibre processing, explicitly scoped to the experimental configurations reported in the primary literature. Within the four-level recycling cycle dataset examined, MRC and rPET exhibit short fibre content (SFC) exceeding 11% after a single recycling cycle-approximately double the virgin baseline of 5.2%-fundamentally destabilising roller drafting mechanics through creation of an uncontrolled floating-fibre population. A threecomponent total drafting force decomposition model (F_D = F_E + F_F + F_T) is developed, validated against published draftometer data, and shown to isolate the transitional slip phase (Stage B, draft ratio 1.1-1.7) as the primary generator of sliver irregularity in high-SFC blends. Within the two gauge settings and four break draft levels studied, the coefficient of variation of the drafting force (CV_D) is minimised at break draft ratios of 1.55-1.75 with the narrower back-gauge setting. A dimensionless lapping risk index R_L = exp[γ(R_a-R_opt)²] is introduced and parametrised for three blend configurations, confirming that surface roughness values outside the 0.6-0.9 μm window generate exponentially increasing adhesion risk via mechanistically distinct failure modes. Microplastic fibre (MPF) shedding across the four recycling levels studied follows a power-law model with exponent δ = 1.322, framing mechanical textile recycling as an environmental paradox. Integration of man-made cellulosic fibres (MMCF) as a carrier matrix is identified as the highest-impact single intervention within the blend ratios tested, enabling recycled cotton content to be doubled from 20% to 40% while maintaining commercial yarn quality thresholds. All models, conclusions, and recommendations are explicitly bounded by the scope of the data from which they are derived.

The architecture of yarn quality monitoring in modern ring spinning mills has historically been anchored to post-process inspection-optical and capacitive sensors within yarn clearers that detect mass deviations only after defective yarn has been formed. This reactive paradigm represents a critical structural deficiency: it identifies the terminal consequences of mechanical failure rather than its genesis, rendering true predictive maintenance fundamentally inaccessible. The present article advances a rigorous theoretical and

Cotton stickiness-arising predominantly from entomological honeydew excreted by phloem-feeding insects onto open bolls-constitutes one of the most economically destructive quality variables in the modern textile manufacturing chain. While the disruptive effects of honeydew contamination on ginning, carding, and ring-spinning operations are relatively well-documented, the compounding downstream consequences across post-spinning operations-automatic winding, warping, sizing (slashing), high-speed shuttleless weaving, circular knitting, and wet processing-remain insufficiently integrated into a single analytical framework. This article synthesises reported regression data, thermodynamic principles governing the phase behaviour of trehalose and melezitose, and documented failure mechanisms across each manufacturing stage to present a holistic, mechanistic model of stickiness-driven quality erosion. Within the experimental configurations surveyed, statistically significant inverse correlations (R² = 0.62-0.81) between thermodetector-based stickiness grade and critical yarn quality parameters-including mass coefficient of variation (CVm%), singlethread tenacity (g/tex, RKM), and nep count (+200%)-are reviewed and contextualised. The causal pathway from sticky fibre to loom downtime, dye unlevelness, fungal staining, and permanent Maillard browning is traced with precision. An advanced enzymatic mitigation strategy employing Aspergillus niger-derived transglucosidase-capable of selectively cleaving the sterically hindered α-(1→1) bond of trehalose and the complex α/β linkages of melezitose under mild thermodynamic conditions (pH 4.5-5.0; 50°C)-is critically evaluated. The analysis concludes with targeted, evidence-based recommendations to support spinning mill operators in blending strategy, instrument selection, and process intervention. All conclusions are explicitly scoped to the blend configurations and measurement methodologies described herein and should not be extrapolated to the broader industry without corroborating data.

This article introduces Textile Information Theory (TIT)-a rigorous mathematical framework that applies Shannon entropy, mutual information, and channel capacity to characterise the fibre-to-yarn spinning process as a noisy information channel. The central problem addressed is the fundamental predictability limit of yarn quality metrics (tensile strength, mass evenness, imperfection counts,

False twisting is one of the most elegant and practically significant mechanisms in mechanical textile spinning. Although the resultant net twist imparted to the fibre strand is zero, the temporary torsional field generated between a constrained delivery nip and a rotating false-twist element creates a transient helical structure that fundamentally transforms a fragile parallel fibre assembly into a mechanically robust, self-locking cohesive bundle. This article presents a comprehensive, mathematically grounded investigation of the underlying physics of false twisting, encompassing torsional mechanics, fibre cohesion through capstan friction, twist propagation as a continuum wave, spinning triangle geometry, compact spinning air-vortex compaction, torsional energy storage and critical buckling, and practical limitations imposed by high machine speeds. Governing equations for each phenomenon are derived and presented in formal notation. Six original analytical plots are included to visualise key functional relationships. The article separately addresses false-twisting mechanisms in the speed frame (flyer crown) and in ring frame modifications (compact spinning and core-spun yarn systems), followed by a structured discussion of direct practical benefits to spinning plant operators. Limitations of the mathematical model, directions for future research, a consolidated nomenclature table, and complete references are also provided.

The Annals of Communications in Mathematics (ISSN 2582-0818, Online) is an international peer-reviewed journal dedicated to publishing high-quality original research papers and invited survey articles in all areas of Pure and Applied Mathematics.

✨ Volume Information (V9N1) (2026)
✔ Papers: 16
✔ Authors: 29
✔ Countries: 09

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The Annals of Communications in Mathematics (ISSN 2582-0818, Online) is an international peer-reviewed journal dedicated to publishing high-quality original research papers and invited survey articles in all areas of Pure and Applied Mathematics.

✨ Volume Information (V8N4) (2025)
✔ Papers: 08
✔ Authors: 12
✔ Countries: 06

✨ Why Publish With Us?
✔ International academic platform
✔ Peer-reviewed research publication
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Indonesia's economy plays an important role in supporting national development and government policies in various sectors such as education, health, and infrastructure. In the first quarter of 2024, Indonesia's economy experienced an increase from the same period in 2022. East Kalimantan experienced significant growth supported by the mining sector, metal industry, and the National Capital City project. However, East Kalimantan is dependent on raw material exports and faces challenges in economic transformation. The government aims to increase exports of processed products to reduce poverty and unemployment. This study analyzes whether economic growth in IKN affects the economy of East Kalimantan, by considering inflation, CPI, export value, and GRDP. This study uses quantitative research methods using Autoregressive Distributed Lag (ARDL) with the advantage that it can be used in models with different levels of stationary and does not matter the number of samples with the data used is secondary data from BPS. The best model obtained is ARDL (3, 3, 4, 3, 4) based on the smallest AIC value which shows the long-term and short-term relationship. Economic growth, export value, and GRDP from the previous quarter affect growth negatively, while GRDP from the same period and the previous quarter affect growth positively. In the long run, export value and GDP significantly affect growth. These results provide insights for the government in managing East Kalimantan's growth, supporting sustainable development and SDG achievement. The results of this study are expected to be a reference for the central government to make policies related to factors that affect Economic Growth in the hope of increasing economic growth in East Kalimantan.

Decentralized Finance (DeFi) has produced two foundational primitives for on-chain trading: bonding curves, which price tokens deterministically against a reserve, and Automated Market Makers (AMMs), which price swaps against a shared liquidity pool. This paper traces the lineage from discrete-token fundraising (ICOs) through bonding curves and constant product AMMs to Uniswap V3, whose concentrated-liquidity design allows liquidity providers to deploy capital over a custom price range. Building on an observation by Lambert, we derive the equivalence between a narrow-range Uniswap V3 position and a covered call (or, by put-call parity, a cash-secured put), with accrued fees serving as the option premium. Because liquidity positions have no maturity, the resulting instrument is a perpetual option. We illustrate the construction with a simulation on the ETH/DAI pair.

The Annals of Communications in Mathematics (ISSN 2582-0818, Online) is an international peer-reviewed journal dedicated to publishing high-quality original research papers and invited survey articles in all areas of Pure and Applied Mathematics.

✨ Volume Information (V3N3) (2020)
✔ Papers: 6
✔ Authors: 15
✔ Countries: 4

✨ Why Publish With Us?
✔ International academic platform
✔ Peer-reviewed research publication
✔ Covers all fields of Pure & Applied Mathematics
✔ Plagiarism screening through Similarity Check / iThenticate
✔ No publication or page charges
✔ Rapid and professional editorial process

Statistical hypothesis testing is the backbone of quality engineering in textile spinning, yet its algebraic formalism-Z-scores, t-values, F-ratios-is routinely applied as a black-box ritual disconnected from physical meaning. This paper argues that the geometric interpretation of classical inference provides textile quality engineers with a uniquely transparent, intuitive, and scalable framework for understanding why statistical tests behave the way they do and how to exploit that behaviour in process monitoring and product qualification.

We test whether projections of the E8 root system's 6,720-edge network onto the Earth's surface align with sparse geographic catalogs beyond what chance permits. From 270 random 8→3 orthonormal projections tested against 160 sacred sites using a best-of-search Monte Carlo null model (1,000 trials each), four projections survive Bonferroni correction with p < 0.05 and effect sizes d = 2.13–3.52. The alignment is a fine-structure phenomenon: specific E8 edges run within 1–11 km of specific sites at orientations requiring 2–3° precision.

Two rounds of synthetic projection engineering (200 matrices matching confirmed seeds' dimension fingerprint, a second round matching inter-row-angle patterns) demonstrate that the mechanism cannot be reduced to any structural property of the projection matrix (cross-validated classifier AUC = 0.52, chance level). Shape controls confirm E8 specificity within the tested set: Fibonacci spheres (n = 240, 600) and 120-cell polytope projections (20 seeds) fail comprehensively under search-aware null models, with RMS values 85–150× worse than E8.

Independent geophysical replication using Indo/Atlantic mantle hotspots (36 sites, zero overlap with sacred sites) yields significant alignment at p = 0.005 (seed 68). Sacred-sites seed 46 cross-replicates on hotspots (p = 0.025), providing the first cross-catalog replication in this study. Additional sparse datasets (plate boundaries, earthquake epicentres, subduction zones) show significant RMS-level alignment at p = 0.010–0.020. Dense catalogs (n ≥ 300) produce flat landscapes with no signal — a sparsity principle constraining the phenomenon to a density regime of roughly 30–160 sites relative to E8's 6,720-edge network.

Version 2.1.0 adds a closest-neighbour 8D shape control: a 50-seed pilot of D₈ root-system projections (112 roots, 1,344 canonical edges; D₈ ⊂ E8) was run on both the 160-site sacred catalog and the 36-site Indo/Atlantic hotspot catalog using the identical pipeline. No D₈ seed reached p < 0.05 on either catalog (best p+ = 0.104 and 0.095 respectively). This strengthens the "E8-specific within the tested set" claim against the strongest available 8-dimensional control. The closest neighbour to E8 in 8 dimensions does not produce the alignment signal.

The alignment is statistically robust across independent catalogs and survives every control applied. Its origin remains unknown.

In Network-on-Chip (NoC), most thermal and peak power balancing methods are monitored by centralized power/thermal managers. This increases inter-core communication latency and imbalanced thermal distribution. These factors directly affect the hot spot formation caused by high power densities developed with increasing per-core transistor number. As a result, reliability decreases along with static power dissipation. This proposal aims to introduce hierarchical agents for balancing power and thermal distribution by manipulating system's parameters such as power, thermal, voltage below the optimal values. As some level of control is applied, this proposal also targets to achieve network scalability by implementing some level of independencies; self-organize and self-optimize distributed agent in overcoming core-level homogeneous processing element (PE) thermal and power variations at runtime. The aims of this work are to significantly contribute to achieving runtime thermal and power balancing, power and thermal management and reducing thermal hot spot formation in NoC.

Background : One of the world's largest developing nations, India, has seen tremendous economic progress since the Liberalization Reforms in 1991, but rather than functioning independently, the market was impacted by several macroeconomic factors that were active simultaneously.
Purpose : The study examined how various macroeconomic factors have affected the SENSEX’s performance in India between 1980 and 2020.
Methodology : Secondary data regarding the stock market and the Reserve Bank and World Bank reports have been considered.
Findings : The Indian stock market and inflation were inversely correlated, while GDP growth and inflation were directly correlated. The foreign currency rate varies with respect to US dollars.
Practical Implications : This research filled in important gaps in the literature regarding the relationship between the stock market, macroeconomic factors, and economic development. It also offered suggestions for investors and organizations on how to analyze and forecast the movement of Indian stock markets, as well as theoretical insights for future forecasts.
Research Originality : While the previous research has addressed the singular impact of variables or included the pre-liberalization period, this study has provided an analysis of stock market data using multiple macroeconomic factors during the post-liberalization period.
Keywords : Indian stock market development, economic growth, BSE, NSE, GDP, exchange rate

This document constitutes an authoritative reference appendix to the companion paper Parametric vs. Non-Parametric Statistical Tests: A Unified Framework for Hypothesis Selection in Textile Spinning Quality Engineering (Balasubramanian, 2026). While the companion paper establishes the theoretical and decision-framework foundations, this appendix provides deep, metric-by-metric guidance covering 10 critical quality parameters across fibre, yarn, cot/apron, and process domains in ring-frame, compact, and air-jet spinning.
For each metric, the following are provided: the physical interpretation of the metric, its typical statistical distribution in production data (with mathematical justification), key distributional parameters, graphical evidence (histogram, Q-Q plot, control chart, and/or comparative plot), recommended primary and alternative statistical tests, process capability guidance, and specific cautions for spinning engineers.

We establish a fundamental connection between information acquired by a decision-maker and the maximal expected profit achievable in finite stochastic resource games. We formalize the player as an information engine analogous to Maxwell’s demon acting on a finite microstate space given by the ordered shoe of decks. Our main result proves that the maximal achievable expected value under any admissible betting policy is bounded above by a positive multiple of the mutual information between the player’s observations of the game X and the true microstate Ω.

We show three supporting lemmas connecting expected value to KL divergences, posterior entropy reduction to mutual information, and a Landauer-style erasure lemma describing shuffle resets. We also provide a toy-model computation verifying the linear approximation EV≈αI for small information, a Monte Carlo recipe for generating numerical approximations of information inherent to real-world games, and two applications of the theorem towards practical planning and decision-making for the advantage player. Our goal is to develop a rigorous basis for describing information-to-profit conversion for exploitable casino games, as well as a meta-strategy for allocating finite resources of time, risk tolerance, travel budget, and cognitive load to maximize long-term bankroll growth.

Whole of the physics and engineering depends upon differential equations, their laws dominate electronics, mechanical and civil engineering. Independent use of differential equations makes it perfect tool for the use of applied mathematics. Here we are discussing some aspects of the differential equations their definitions, types of solutions, their applications and uses.

The Imprinted Curvature Hypothesis (ICH) is presented here as a conservative geometric framework within unmodified General Relativity. The basic idea is that a weak, ultra-longwavelength curvature imprint may have been encoded in the initial spatial geometry of the early universe and could persist as a frozen large-scale bias under standard cosmic evolution. ICH does not introduce new particles, new propagating fields, or modified gravitational dynamics. The Einstein field equations and standard matter conservation remain unchanged. Instead, the imprint is treated as part of the admissible initial data on an early spacelike hypersurface. In this picture, exact Friedmann-Lemaître-Robertson-Walker geometry remains the limiting case, while the imprint represents a weak and subdominant departure from exact conformal flatness on ultra-large scales. The framework is developed using the standard Einstein equations, the 3+1 (ADM) decomposition, and the associated constraint structure, with its large-scale persistence interpreted through the usual conservation logic of adiabatic curvature perturbations. The paper has four main aims: to define the model clearly, clarify its gauge interpretation, establish its consistency within General Relativity, and connect it to observationally testable signatures. Within this framework, the imprint is not expected to produce localized mass-like clumps or dominant local effects. If it has an observational role, that role should instead be weak, coherent, and statistical. The most relevant channels include large-scale weak-lensing residuals, smooth voidrelated signatures, faint anisotropy tests, and topology-linked structure in the cosmic web. One specific possibility examined here is that extreme quasars may show a statistically enhanced association with cosmic-web nodes identified through large-scale structure reconstruction. The purpose of this work is to define ICH as a falsifiable geometric framework with weak, largescale, subdominant effects that remain compatible with precision cosmology. Under that interpretation, ICH offers a testable way to ask whether a suppressed primordial curvature imprint could contribute to selected large-scale cosmological residuals in the Euclid era and beyond.

Several real-world phenomena emerging in engineering and science fields can be described successfully by developing certain models using fractional-order partial differential equations. The exact, analytical, semi-analytical or even numerical solutions for these models should be examined and investigated by distinguishing between their solvablities and non-solvabilities. In this paper, we aim to establish some sufficient conditions for exploring the existence and uniqueness of solution for a class of initial-boundary value problems with Dirichlet condition. The gained results from this research paper are established for the class of fractional-order partial differential equations by a method based on Lax Milgram theorem, which relies in its construction on properties of the symmetric part of the bilinear form. Lax Milgram theorem is deemed as a mathematical scheme that can be used to examine the existence and uniqueness of weak solutions for fractional-order partial differential equations. These equations are formulated here in view of the Caputo fractional-order derivative operator, which its inverse operator is the Riemann-Louville fractional-order integral one. The results of this paper will be supportive for mathematical analyzers and researchers when a fractional-order partial differential equation is handled in terms of finding its exact, analytical, semi-analytical or numerical solution.

Cluster analysis has been generally used as an efficient tool in the quantitative estimation of genetic diversity for a breeding programme (divergence analysis), grouping of different genotypes of a particular crop and it is more useful in choosing suitable parents for heterosis breeding. Clustering techniques aims to group data according to common properties. This grouping is often based on the distance between the data. Clustering techniques are divided into hierarchical and non-hierarchical methods according to the fragmentation technique of clusters. There are various clustering methods which come under these techniques viz., single linkage, complete linkage, average linkage, Ward's method and Tocher method. The efficiency of the techniques and methods are given less importance. In this context an attempt was made in this paper for the comparative study of the different clustering techniques and methods in small samples. The cluster validation techniques are used for the efficiency measurements of these methods. The results of the analysis are presented comparatively at the end of the study and which methods are more convenient for data set is explained.

Cluster analysis has been generally used as an efficient tool in the quantitative estimation of genetic diversity for a breeding programme (divergence analysis), grouping of different genotypes of a particular crop and it is more useful in choosing suitable parents for heterosis breeding. Clustering techniques aims to group data according to common properties. This grouping is often based on the distance between the data. Clustering techniques are divided into hierarchical and non-hierarchical methods according to the fragmentation technique of clusters. There are various clustering methods which come under these techniques viz., single linkage, complete linkage, average linkage, Ward’s method and Tocher method. The efficiency of the techniques and methods are given less importance. In this context an attempt was made in this paper for the comparative study of the different clustering techniques and methods in small samples. The cluster validation techniques are used for the efficie...

Salah satu ciri pengajaran berkesan ialah kepelbagaian dalam kaedah pengajaran dan pembelajaran di dalam kelas. Kepelbagaian dalam kaedah pengajaran bertujuan untuk memberi pengalaman pengajaran dan pembelajaran yang bermakna kepada para pelajar malah meningkatkan motivasi mereka untuk belajar. Melihat kepada kepentingan penggunaan pengkaedahan ini, maka pengkaji terdorong untuk mengkaji bentuk kaedah pengajaran dan pembelajaran yang diamalkan oleh lapan orang Guru Cemerlang Pendidikan Islam (GCPI) yang mengajar di pelbagai jenis sekolah menengah di luar bandar dan bandar sebagai satu kajian perbandingan. Hasil dapatan data soal selidik menunjukkan bahawa terdapat kecenderungan yang serupa dalam penggunaan kaedah pengajaran dan pembelajaran GCPI di sekolah menengah luar bandar dan bandar. Pada bahagian akhir kertas kerja ini, beberapa cadangan juga dikemukakan bagi meningkatkan penggunaan kaedah pengajaran dan pembelajaran yang lebih pelbagai di sekolah luar bandar dan bandar. Kata ...

A major limitation of fuzzy or neuro-fuzzy systems is their failure to deal with high-dimensional datasets. This happens primarily due to the use of T-norm, particularly, product or minimum (or a softer version of it). Thus, there are hardly any work dealing with datasets with dimensions more than hundred or so. Here, we propose a neuro-fuzzy framework that can handle datasets with dimensions even more than 7000! In this context, we propose an adaptive softmin (Ada-softmin) which effectively overcomes the drawbacks of "numeric underflow" and "fake minimum" that arise for existing fuzzy systems while dealing with high-dimensional problems. We call it an Adaptive Takagi-Sugeno-Kang (AdaTSK) fuzzy system. We then equip the AdaTSK system to perform feature selection and rule extraction in an integrated manner. In this context, a novel gate function is introduced and embedded only in the consequent parts, which can determine the useful features and rules, in two successive phases of learning. Unlike conventional fuzzy rule bases, we design an enhanced fuzzy rule base (En-FRB), which maintains adequate rules but does not grow the number of rules exponentially with dimension that typically happens for fuzzy neural networks. The integrated Feature Selection and Rule Extraction AdaTSK (FSRE-AdaTSK) system consists of three sequential phases: (i) feature selection, (ii) rule extraction, and (iii) fine tuning. The effectiveness of the FSRE-AdaTSK is demonstrated on 19 datasets of which five are in more than 2000 dimension including two with dimension greater than 7000. This may be the first time fuzzy systems are realized for classification involving more than 7000 input features.

In this paper, a compact triple band metamaterial antenna based on modified electric-field coupled (ELC) resonator is presented. The modification to the conventional ELC is achieved by the use of strip lines to enhance the capacitive coupling of the capacitive gaps and a stub printed at the back of the resonator. The unit cell’s macroscopic parameters were not affected by the structural modifications as the electric moment dominates the magnetic moments in the ELC response. By employing this structure, three resonance frequencies at 1.65 GHz, 3.5 GHz and 5.8 GHz are obtained. The overall size of the antenna is 40 mm × 45 mm (0.22λo × 0.24λo) with the unit cell size of 12 mm × 11 mm (0.066λo × 0.060λo) at 1.65 GHz. The peak gain of 2.10 dBi and radiation efficiency of 97% is obtained at 5.8 GHz. The proposed antenna has advantages of being compact, small and suitable for WiMAX (3.5 GHz) and WLAN (5.8 GHz) applications. The simulated and measured return losses and the radiation patter...

We build on the theoretical foundation established in "The Continuous Complex Normal Family and Its Phase-Coherent Maximum-Likelihood Estimator" (McCloskey, 2026) and empirically verify the finite-sample performance and practical robustness of the phase-coherent likelihood (PCL) estimator 𝛼 ̂𝑛. We conduct an extensive Monte Carlo study across various sample sizes in two scenarios: pure Gaussian noise and weak latent sinusoidal modulation calibrated to realistic interferometric residuals. Our results demonstrate that 𝛼 ̂𝑛 is unbiased to machine precision under the null hypothesis, with standard deviation decaying as 𝑂 (1 √𝑛) and 95% Wald coverage converging rapidly to nominal levels in both scenarios. In the presence of latent phase structure, bias vanishes by 𝑛 = 500 despite a signal amplitude of only 0.2 inside unit-variance noise, and the estimator reliably recovers the true slope 𝛼 0 ≈ 𝜋. These findings provide the first rigorous empirical confirmation of the PCL's effectiveness and robustness, establishing it as a practical tool for detecting hidden oscillatory phenomena in continuous complex probability models. Explicit appendices supply the code that was used to generate the Monte Carlo simulations as well as the closed-form Hessian and per-observation score contributions that enable direct sandwich variance estimation.

Accurate prediction of weapon effectiveness in ballistic engagements requires thorough modeling of both deterministic projectile dynamics and the stochastic uncertainties that arise from manufacturing tolerances, atmospheric variability, guidance noise, and target motion. Currently existing approaches to resolve these issues typically treat these components separately. Exterior ballistics models focus on deterministic trajectory prediction, while dispersion analysis relies primarily on Monte Carlo simulation or empirical error models. We present a model for applied ballistics based on stochastic differential equations (SDEs) that directly propagate uncertainties through projectile dynamics. The model describes projectile motion as a stochastic dynamical system in which aerodynamic forces, environmental disturbances, and system parameter uncertainties are represented as random processes. From this starting point, probability density functions of impact location can be derived to allow closedform or semi-analytical estimation of relevant dispersion metrics such as circular error probables (CEP) and probabilities of kill (PK). The model is applicable to a wide variety of unguided artillery, rockets, guided missiles, and surface-to-air intercept systems, as well as military engagements involving single maneuvering targets. Numerical examples are given in order to demonstrate how the model provides a consistent method for evaluating engagement outcomes across widely different ballistic systems. By integrating stochastic dynamics with engagement-level lethality metrics, the proposed approach offers a mathematically coherent alternative to purely simulation-based dispersion analysis. This capability should prove particularly valuable for weapon system design and military engagement planning.

In this paper, we study a special case of the Jesmanowicz equation with exponents that are multiples of four. Using elementary number theory methods, including greatest common divisor analysis and infinite descent, we show that the equation admits no non-trivial positive integer solutions in this case. The approach is based on structural properties of the equation and provides a simplified perspective on this restricted setting.

We test whether projections of the E8 root system's edge network onto Earth's surface align with 160 sacred and energetically significant sites beyond what chance permits. From 270 random 8D to 3D orthonormal projections, each independently optimized over a three-parameter orientation space (latitude, longitude, bearing), four projections survive a best-of-search Monte Carlo null (1,000 trials each) with Bonferroni-corrected p < 0.05 across five quantile thresholds. The four confirmed seeds exhibit distinct alignment signatures—breadth (96.9 to 97.5 percent of sites within 11 kilometers), precision (83.1 percent within 5.6 kilometers), and ultra-precision (48.1 percent within 2.2 kilometers)—with effect sizes of d = 2.13 to 3.52.

Perturbation analysis reveals sharp RMS wells at each optimum: a 5-degree displacement in any orientation parameter increases RMS by 44 to 72 percent, while null optima show near-zero sharpness (z = 4.1 to 6.8, all p < 0.005). A random-site control confirms the signal is site-dependent (Fisher's combined p = 0.007), with the sacred-site catalog producing 5.7 to 18.5 percentage points of sharpness excess above a ~47 percent geometric baseline.

Systematic characterization of the 270 projection matrices (cross-validated AUC = 0.52, indistinguishable from chance) and on-sphere edge network topology (all aggregate metrics identical between confirmed and failed seeds) demonstrates that the signal cannot be attributed to any property of the projection or its output geometry. The alignment resides in the precise angular relationship between individual E8 edges and individual site locations—a fine-structure correspondence visible only at the 0.01 to 0.10 degree scale and destroyed by orientation perturbations of 2 to 3 degrees.

The signal is statistically robust against every test applied. Its origin remains unknown. A subset analysis using a related 62-site catalog (77 percent overlap) finds that the confirmed seeds do not transfer at their fixed orientations, but a fresh tournament identifies a different significant seed (RMS p = 0.002, d = 3.87; ≤0.05 degree Bonferroni p = 0.020), consistent with the fine-structure interpretation that different site arrangements resonate with different projections. We discuss potential explanations including site-catalog spatial structure, E8 symmetry group effects, and a five-level research programme for mechanism isolation.

This study examined test alignment of entry qualifications as predictors of final grades of students in tertiary institutions in Nigeria. Four research questions and hypotheses were formulated for the study and tested at .05 alpha level using regression statistical technique. The entry qualifications and final grades of 2,504 final year students were randomly sampled from 12 tertiary institutions in Nigeria and used as the data for the study. The findings of the study showed that the entry qualifications (WASSCE, NECO, NBTCE and UTME) are not effectively aligned with the courses of students in tertiary institutions to ensure good final grades. It was concluded that alignment should be adopted and implemented effectively since test alignment of entry qualifications with courses of students in tertiary institutions is very important as it can be used to ensure and predict good final grades of students. It was recommended among others that what students learn in secondary schools should be built upon in tertiary institutions rather than learning starting from a totally different point that is abstract to the students because students' interest and enthusiasm would be developed and maintained leading to effective learning and better academic achievements.

While the mathematics that was developed in Theoretical Framework for Ace Location in Blackjack (McCloskey, 2026) produced model-specific displacement probabilities and established the exponential decay of pairwise positional correlations, the author deliberately stopped short of providing a field-ready model-agnostic estimation procedure. The present work supplies that missing practical implementation. Numerical examples for riffle shuffles on single-deck and double-deck shoes confirm the phase transition predicted by the GSR and geometric-packet models. One should be able to quickly use the recipe outlined in this paper to determine from observed casino shuffles whether that shuffle is trackable.

Recent studies on the global ideology of public housing are significantly focused on the cultural values of inhabitants. Thus rapid transformation of originally design housing units that are based on modern standards by inhabitants is widespread. The emic and etic principles was used to evaluate existing situation where indigenous culture inclusive housing demand is on the rise. Retrospectively, established principles of emic and etic concept in directing public housing design was measured to test the synthesis- an interphase thought to provide sustainability amidst conflicting indigenous space demand and regulated homogenous designs. The study uncovered a chaotic but culture-specific genesis that comprise of formalized antecedents that can no longer be ignored, but lacks standardisation. Instead, the etic and emic interphase (convergences) remains a delusion proffering unintended solutions. Implacably, rigour in the concept of culture bonds sustainability process in public housing,...

The outbreak of the COVID-19 pandemic has necessitated the shift from face-to-face lecture delivery to online mode of delivery in most countries across the world including Ghana. There is the growing need to study the patronage of the students in online learning to improve practice. The data of 323 observations consisting of first and second year students was collated by virtual learning team of Ada College of education, Ghana. Multinomial regression was used for the analysis. The dependent variable had 3 levels and the predictor variables were sex and programme of study with 2 and 3 levels respectively. Female students were found to be 0.784 times more likely than males to have smart phone but with no access to online lectures. Primary education students were found to be 1.287 times less likely to belong to the category of students with no smart phone to access online lesson than the reference category of students with smart phone that have access online lesson. Students who offer visual arts programme were found to be 1.420 times less likely to belong to the category of students with no smart phone to access online lesson than the reference category. It was also found that students who study degree in mathematics as a major were 1.423 time less likely to have a smart phone but no access to online lessons than the reference category. The study recommended for the management of the college to consider the findings of this research to offer hard copy notes, exercises and assignments to the identified students with low patronage of online learning.

and David Beirens de Haan (1847) published work containing some interesting integrals. While no formal derivations of the integrals in his book Nouvelles Tables d'Intégrales Défines are available in current literature deriving and evaluating such formulae are useful in all aspects of science and engineering whenever such formulae are used. Formulae in the book of Bierens de Haan are used in connection with certain potential problems where there is the need to determine the vector potential of two parallel, infinitely long, tubular rectangular conductors carrying cur-rents in opposite directions. In this current work we supply formal derivations for some of these integrals along with deriving some special cases as new integrals in order to expand upon the book of Bierens de haan to aid in potential research where these formulae are applicable. Updating book of integrals is always a useful exercise as it keeps the volume accurate and more useful for potential readers and researchers. Formal derivations are also useful as they help in verifying the correctness of integrals in such volumes. The definite integral we derived in this work is given by in terms of the Lerch function, where the parameters a, k, m, λ and p are general complex numbers subject to their restrictions. This formal derivation is then used to derive the correct version of a definite integral transform along with new formulae. Some of the results in this work are new.

A relation is a mathematical tool for describing set relationships. Relationships are common in databases and scheduling applications. Science and engineering are designed to help humans make better decisions. To make these choices, we must first understand human expectations, the outcomes of various options, and the degree of confidence. With all of these data, partial orders will be generated. In several fields of engineering and computer science, partial order and lattice theory are now widely used. To mention a few, they are used in cloud computing (vector clocks, global predicate detection), concurrency theory (pomsets, occurrence nets), programming language semantics (fixed-point semantics), and data mining (concept analysis). Other theoretical disciplines benefit from them as well, such as combinatorics, number theory, and group theory. Partially ordered sets emerge naturally when dealing with multidimensional systems of qualitative ordinal variables in social science, especially to solve ranking, prioritising, and assessment concerns. As an alternative to standard techniques, partial order theory and partially ordered sets can be used to generate composite indicators for evaluating well-being, quality of life, and multidimensional poverty. They can be applied in multi-criteria analysis or for decision-making purposes in the study of individual and social desires, including in social choice theory. They're also valuable in social network analysis, where they may be utilized to apply mathematics to explore network topologies and dynamics. The Hasse diagram method, for example, produces a partial order with multiple incomparabilities (lack of order) between pairs of items. This is a common problem in ranking studies, and it can often be avoided by combining object attributes that lead to a complete order. However, such a mix introduces subjectivity and prejudice into the rating process. This work discusses the notion of a f -prime radical of a partially ordered set with respect to ideal. In posets, we investigated the concept of f -primary ideals. It is investigated how to characterise f -primary ideals in relation to f -prime radicals. In addition, an ideal's f -primary decomposition is constructed.