.
Analysis of Lateral Offset Invariance in Parallel Parking Maneuver: A Geometric Simulation Study
Kevin Luo and Hsinghan Meng,Sunny Hills High School, Fullerton, CA 92833, SAT Professionals, Diamond Bar,CA 91765
ABSTRACT
This paper investigates whether the initial lateral offset of a vehicle from theparking space, denoted ∆y, affects the vehicle’s ability to successfully complete a parallelparking maneuver. Using the geometric mathematical model developed by Wahab et al.[1] and implemented via a simulation developed in a Java-based environment to allow forhigh-fidelity kinematic modelling and real-time geometric validation, a series of trials wereconducted in which ∆y was systematically varied while all other vehicle and parking spaceparameters were held constant. The results demonstrate that, under the constraints of thismodel, the parallel parking maneuver can be completed successfully across a wide range of ∆yvalues. Specifically, varying ∆y causes the geometric solution to self-adjust: the intermediatequantities a, c, y1, and θ all recalculate such that a valid two-arc trajectory always exists.It is concluded that ∆y does not prevent a vehicle from parking; rather, it only shifts thestarting position and arc geometry whi e preserving the feasibility of the maneuver
KEYWORDS
parallel parking, path planning, lateral offset, ∆y, simulation, Ackermann steer
ing, bicycle model.
The Illusion of Cybersecurity A Systematic Review of Dynamic Threat Profiles, Attacker Economics, and Adaptive Defense Equilibria
David Mpunwa, ESAMI, Namibia
ABSTRACT
Security teams love the word “hardened.” It is comforting — it suggests permanence, the sense that once a firewall goes up and multi-factor authentication is switched on, the job is finished. That comfort is the problem. This review argues that cybersecurity is not a fixed state but a moving equilibrium, one where attacker economics and defender investment continuously recalibrate against each other. Drawing on the Gordon–Loeb framework and recent evidence on corporate disclosure and reconnaissance costs, the paper traces how commodified cybercrime — ransomware-as-a-service, initial access brokers, dark-web data markets — has collapsed the technical barrier to entry for serious attacks. Core controls (cryptography, multi-factor authentication, VPNs) are mapped against the CIA Triad to show why compliance checklists routinely mistake a snapshot for a state. A layered, Zero-Trust-anchored mitigation roadmap closes the paper.
KEYWORDS
Cybersecurity, Zero Trust Architecture, Threat Actor Economics, Defense-in-Depth, Digital Forensics
The Pyramidal Harmonic Series: Empirical Verification of the Universal Moiré Matrix and Wave Pattern Mathematics
Mark Lance Moody , United States of America
ABSTRACT
Classical wave mechanics rely on continuous algebraic approximations that compress and obscure underlying geometric structures. This paper presents a deterministic framework that natively generates topological wave functions by observing the explicit, uncompressed arithmetic expansions of cyclical partial fractions. By analyzing the reciprocal expansions of specific generating functions—namely the symmetric spatial dilator (10^9 - 1)^2 = 999,999,998,000,000,001 and the asymmetric phase-shift engine (10^8 - 1)(10^9 - 1) = 99,999,998,900,000,001—we demonstrate that explicit arithmetic cascades act as exact mathematical analogs for amplitude stacking and phase precession. When these uncompressed data streams are evaluated within a modulo-72 boundary condition, the output autonomously renders a two-dimensional Moiré interference lattice. Furthermore, by factoring the cyclic limit, we derive a rigid 81-node phase-space combinatorial grid governed by the prime factors 3, 37, and 333,667. This framework proves that positional arithmetic, when fully expanded rather than algebraically compressed, functions as a zero-entropy holographic tensor network.
Use Of Ai-Based Conversational Agents And Postsecondary Student Adjustment And Persistence: Evidence From A Comparative Study Of Ali And Chatgpt
Bruno Kesangana, 1Department of Teaching and Learning Studies, Faculty of Education Sciences, Université Laval, Quebec City, Quebec, Canada
ABSTRACT
Conversational agents (CAs) are increasingly deployed in postsecondary institutions as accessible, stigma-free supplements to mental health and academic support services. However, the literature rarely distinguishes between institutionally designed, specialized educational CAs and general-purpose large language model (LLM)-based tools such as ChatGPT, treating them as a homogeneous category. This study addresses this gap by comparing Ali — a specialized CA anchored in the Quebec collegiate network — with ChatGPT, a general-purpose LLM, on their relationships with postsecondary student academic adjustment, socio-emotional adjustment, and persistence intentions. Using a quantitative cross-sectional design with 151 students (M_age = 21.86, SD = 1.62; 58.3% female), we conducted ANCOVAs and hierarchical multiple regression analyses. ChatGPT users reported significantly higher competence expectations, perceived value, academic adjustment, socio-emotional adjustment, and persistence intentions. However, regression analyses revealed a more nuanced picture: perceived cost uniquely predicted academic adjustment (β = .196, p = .018); usage duration negatively predicted socio-emotional adjustment (β = −.199, p = .018); and competence expectations predicted persistence intentions (β = .255, p = .012). Moderation analyses showed structurally divergent prediction patterns by CA type: for Ali users, duration, value, and cost positively predicted outcomes, whereas for ChatGPT users, duration negatively predicted socio-emotional adjustment and value showed a negative trend for persistence. These findings challenge the assumption that higher perceived utility translates linearly into better student outcomes and call for tool-specific policies for AI integration in higher education.
KEYWORDS
conversational agents, ChatGPT, Ali, academic adjustment, student persistence, expectancy-value theory, postsecondary education, AI in education