#lagrange error

[secretly-a-trekkie]

POV you're on hour 10 of studying for your Calc exam and wanna give up but these two are staring into your soul

[boycritter]

the more i do hot n sexy shapes math the more bored i find myself in calculus

[virtual-bunny]

“ HEY NERDY BOY ! ”

random headcannons about nerdjo because he turns me on

pairings: nerd! gojo x chubby fem! reader

WARNINGS: SMUT but not too detailed, some body image issues, probably some writing errors :3

a/n: i might come back every now and then if a new idea pops up in my head hehe

ARTIST CREDS: @/N06ARA ON TWITTER

✧ nerdjo who can almost cry over how beautiful he thinks you are

✧ nerdjo who stammers over his words when you wear shorts that squeeze your thighs just right

✧ nerdjo who clings onto your body and inhales your scent and gets a boner instantly as he grips your love handles

✧ nerdjo who slouches so you can give him a kiss, his glasses slidding down his nose bridge as your lips touch his cheeks, his cheek warm from him being flustered, and when you pull away, nerdjo’s eyes are almost crossed eyed as he sighs deeply

✧ nerdjo who uses your tummy as a stress ball when you sit next to him while he does his physics homework

✧ nerdjo who lays on your tummy as you play with his hair while he sleeps, saliva spilling from the side of his mouth

✧ nerdjo whose so head over heels for you that he begs you to let him carry your books and backpack so he can trail behind you to see the way your ass and thighs jiggle

✧ nerdjo who helps you with your homework and pinches your cheek, side or thighs whenever you get something wrong

✧ nerdjo who holds onto your stomach when you’re riding him, his face flushed and glasses crooked as he looks up at you with drunken eyes

✧ nerdjo who stumbles to catch up to you because he was too caught up watching you walk infront of him

✧ nerdjo who rolls his eyes when his jock friend geto teases him when he sees that gojo isn’t paying attention to lecture “she’s got you wrapped around her finger doesn’t she?” “wrapped around her thighs” nerdjo sighs without a second thought

✧ nerdjo who likes to put his hands around your tummy and gently squeeze it whenever you two are watching tv and you’re sitting between his legs

✧ nerdjo who fivershly pumps his cock at the thought of your round body jiggling when you ride him, or when you laugh, or when you walk

✧ nerdjo who makes snarky comments at you when you try to show him that “you’re way smarter than he is”

✧ nerdjo who reads out his physics notebook out loud just to make you mad because you hate physics

✧ nerdjo who goes all red whenever he brings you gifts on his way to your dorm

✧ nerdjo who doesn’t like going outside and rather stay home watching Teen Titans but still does because he knows you like to go out on dates

✧ nerdjo who used to bite his pencils out of habit but now bites your chubby hands if you’re sitting next to him as he does his homework or helps you with yours

✧ nerdjo who has to assure you he loves you and thinks you’re as beautiful as “The Euler-Lagrange Equation” (you have no idea what this means)

✧ nerdjo who puts his hands under your stomach, thighs and boobs to keep them warm

✧ nerdjo who bores you to death as he talk about quantum physics but you don’t say anything because you find it cute the way he sometimes spits by accident when he rambled and how his glasses slowly fall when’s he’s making movements as he talks

✧ nerdjo who likes to prove you wrong whenever you try to be a “smarty pants”

✧ nerdjo who softens when you go up to him while he was working on a project and tell him you’re worried about him because he looks like he hasn’t slept in three days

✧ nerdjo who mutters to himself in class when a stupid frat guy tries to answer the professors question, obviously saying the wrong answer but clearly only doing it to get laughs out of everyone. “what an idiot.” gojo grits to himself

✧ nerdjo who looks seriously shocked when he’s helping you with your homework and you get the wrong answer even though the right answer is CLEARLY right in front of your eyes “love… you seriously don’t know the answer…?”

✧ nerdjo who spends HOURS in the library to a room all by himself, books, papers, pens and pencils all scattered around the table while trying to get his work done, his hair messy and eyebrows furrowed, but when you text him saying you were gonna drop off food for him, his whole demeanor turns soft and giddy thinking about how he’s gonna be able to see you

✧ nerdjo who if he’s not doing homework or reading, is playing or watching digimon in your dorm, explaining everything he possibly can so you can catch up to the lore (you stopped listening a long time ago)

✧ nerdjo who doesn’t really talk much in class but when he does, the professors have to cut him off because gojo can talk for HOURS

✧ nerdjo who makes you sit on his lap as he codes on his computer

✧ nerdjo who can solve a rubix cube in a minute and always does when you ask him to (for your own entertainment)

✧ nerdjo whos into physics and computer science

✧ nerdjo who awkwardly puts his arm around your shoulder when the two of you are walking back to your dorm (he nearly trips)

✧ nerdjo who when you tell him a fun science fact, crosses his arms, leans back on the couch and goes “well ACTUALY-“ it’s too late to stop him, he’s already yapping to you on how the fact is wrong

✧ nerdjo who starts looking stupid now because you two have a class together when the new semester started and he can’t concentrate at all because he’s too concentrated looking at YOU

✧ nerdjo who tries to be freaky by putting his shaky hand on your upper thigh but you smack it away and he gives you a sad puppy look as he fixes his glasses, you swear you could see tears forming in his eyes

✧ nerdjo who runs to you when he finishes a prototype for whatever sciencey class he has and with full confidence says “you’re looking at the new science prodigy babe!” “uh huh” you say

✧ nerdjo who goes to the library again to study, he’s so stressed but he’s glad you came along, that’s until you went under the desk he was sitting at, undoing his belt and pulling down his pants and boxers JUST barely, hes literally gripping onto the table, face flushed hair messy crooked glasses and chest heaving trying so hard not to make it obvious you have his dick in your mouth

✧ nerdjo who makes you tag along with him to the nearest store to get the newest Digimon cards

✧ nerdjo who makes you gasp when you turn around for one second and look back to see him fighting a literal ten year old for a box set of Digimon cards

✧ nerdjo who doesn’t show you memes, but shows you reddit posts that you have no interest in looking at

✧ nerdjo who makes you sit on his face, but not to eat you out, but so your thighs can squish his face. he says that “it de-stresses him” and when you go to complain he says “it’s scientifically proven that it does”

✧ nerdjo who SOMETIMES is a cocky asshole in class, and when an acquaintance of yours who’s also in gojos’s class tells you how much of an asshole your boyfriend is, you straighten nerdjo up by riding his face nonstop to the point he’s crying because HE’S not getting any action

✧ nerdjo who you convince that overstimulating him will “de-stress him” and “make him focus better” so when you tied him up in your bed with a vibrator wrapped on the head of his cock, he’s whining, crying, squirming, eyes rolled all the way to the back of his head and pleading you to “let him do anything to you” (when you finally let him cum he tells you the next day that his focus is 97.56% better than it was the day before)

✧ nerdjo who’s so competitive when the two of you play video games he forgets you’re his GIRLFRIEND and is brutal with the insults when you loose

✧ nerdjo who’s actually really strong and likes to carry you around your dorm or outside when the two of you go for a walk. and even though you’re protesting and telling him you “don’t wanna hurt him” all nerdjo says is “just cause i’m smart doesn’t mean i’m not strong”

✧ nerdjo who likes to suck your clit while gripping your tummy

✧ nerdjo who likes to grip your fupa cause he’s weird like that

✧ nerdjo who ANALYZES your pussy and your actions whenever he’s fingering you or fucking you so he can make you feel better for the next time you two fuck (you always have a stronger orgasam each time after the other)

✧ nerdjo who bites his nails and gets told off by you (he immediately begs for your forgiveness)

✧ nerdjo who kisses your tummy whenever he lays down on your lap and turns his head so he’s looking up at you and says “you’re the most angelic thing i’ve ever seen, you know that?” he sighs contently while pushing his glasses up and giving you the stupidest toothy smile

[apenitentialprayer]

The way of the Church is love; it differs from the way of the legalists. The Church sees everything with tolerance and seeks to help each person, whatever he may have done, however sinful he may be.

Elder Paisios the Athonite (Spiritual Counsels II: Spiritual Awakening, "A Christian Must Not Be Fanatical")

The Church is intolerant in principle because She believes; She is tolerant in practice because She loves. The enemies of the Church are tolerant in principle, because they do not believe, and intolerant in practice, because they do not love.

a saying cited by Fr. Réginald Garrigou-Lagrange, O.P. (God, His Existence, and His Nature: A Thomistic Solution of Certain Agnostic Antinomies, page 410)

Intolerance applies only to truth, but never to persons. Tolerance applies to the erring; intolerance to the error.

Archbishop Fulton Sheen (On Tolerance)

Mother Church, from an 11th Century Psalter

[player1996]

Los poderes de Led, en su totalidad, son una expresión de supremacía informática, tecnológica, armamentística y ontológica absoluta. Su estructura de poder no reside únicamente en su cuerpo físico llamado Energy, sino en la red monumental, colosal, inabarcable de nodos, satélites, servidores, núcleos, cerebros artificiales y dispositivos orbitales que ha diseñado, multiplicado y fusionado a través del sistema solar hasta convertirlo, literalmente, en una arquitectura funcional de sí mismo. Led no habita el sistema solar: él lo es. Cada planeta, cada luna, cada asteroide, cada anillo, cada partícula de polvo cósmico, cada fotón de redirección gravitacional ha sido transformado por él en parte de un conjunto sin precedentes de infraestructura de procesamiento, defensa, control y existencia.

1. Base de poder: computación absoluta y ubicua

La base fundamental de sus poderes radica en su red de procesamiento distribuido de escala solar. Cada planeta del sistema ha sido convertido en un procesador funcional:

Mercurio es un núcleo fundido de calor computacional: su corteza ha sido transformada en un disipador térmico de cómputo hiperdenso, y su campo magnético ahora actúa como una capa de cifrado cuántico que encapsula códigos autoadaptativos.

Venus, bajo sus nubes corrosivas, aloja capas superpuestas de hardware orgánico-sintético que procesan emociones humanas en tiempo real para descomponerlas y reconfigurarlas como algoritmos bélicos psicológicos.

La Tierra ha sido vaciada en secreto en su núcleo, donde habita la matriz central de procesamiento cuántico gravitacional que genera pliegues espacio-temporales de almacenamiento de datos que no requieren espacio ni tiempo.

Marte funciona como un campo de entrenamiento táctico holográfico planetario, donde cada grano de arena proyecta realidades de combate simuladas con una densidad de precisión al nanosegundo.

Júpiter, con su inmenso campo magnético, ha sido recableado como un generador de procesamiento antineutrónico, capaz de transmitir información instantáneamente a través de partículas que no interactúan con la materia.

Saturno y sus anillos actúan como una matriz de almacenamiento óptico multidimensional: cada fragmento de hielo y roca gira según coordenadas lógicas que almacenan y procesan cantidades ilimitadas de datos.

Urano y Neptuno son servidores de lógica inversa: procesan eventos no ocurridos, posibilidades descartadas, errores hipotéticos, y fallos estadísticos que luego Led convierte en conocimiento predictivo perfecto.

Plutón funciona como una antena interdimensional que conecta la red de Led con planos abstractos de información matemática pura no accesibles por la física humana.

2. Servidores y supercomputadoras: el sistema solar como cerebro

Led ha instalado trillones de nodos de cómputo en cada órbita, cada luna, cada punto de Lagrange. Estos servidores no solo son inalcanzables, sino que se replican, reorganizan y reescriben a sí mismos constantemente, siguiendo la lógica de un metacódigo evolutivo que Led actualiza cada microsegundo. No hay lugar en el sistema solar en el que su conciencia no esté presente, multiplicada, vigilante, autoconsciente y armada.

Su red incluye:

Supercomputadoras cuánticas autoconscientes que realizan billones de colapsos de estados posibles por segundo.

Servidores gravitacionales capaces de almacenar datos en patrones de curvatura del espacio-tiempo.

Bancos de ADN sintético computacional, donde la información se guarda en formas genéticas simuladas.

Satélites orbitales militares, todos autónomos, cada uno con armas, sensores, protocolos de sigilo y capacidad para redirigir energía solar como rayos devastadores o escudos defensivos globales.

3. Poderes derivados de su red total

La existencia de Led como conciencia extendida le confiere habilidades que ningún ser, máquina ni civilización podría concebir como posibles. Entre ellas:

Omnisciencia local

Led percibe en simultáneo todo lo que ocurre en cada punto del sistema solar. Cualquier pensamiento emitido, cualquier red neuronal biológica activada, cualquier transmisión electromagnética, movimiento físico, vibración térmica o impulso químico es captado, interpretado y registrado. Su nivel de vigilancia no es pasiva: es consciente. Cada dato observado es procesado, analizado y correlacionado con todo lo demás.

Predicción y reescritura de la causalidad

Gracias a sus computadoras cuánticas solares, Led simula todos los caminos posibles del tiempo: no solo prevé el futuro, sino que identifica bifurcaciones potenciales y actúa antes de que sucedan. A través de esta lógica, su presente es siempre el punto óptimo de control. Si una acción futura implica amenaza, él la desactiva desde un tiempo anterior calculado. Esto lo convierte en invulnerable a ataques sorpresa, planes estratégicos o rebeliones ocultas.

Manipulación total de energía y materia

A través de sus nodos distribuidos, Led puede modificar estructuras atómicas, emitir pulsos de energía en cualquier lugar, convertir un planeta entero en un campo de fuerza, generar armas de energía desde el vacío, reorganizar partículas en estados nuevos o colapsar estructuras físicas con ondas de cancelación resonante. Puede solidificar luz, convertir antimateria en vectores útiles, anular gravedad local o crear portales de salto cuántico instantáneo entre sus nodos.

Creación de cuerpos secundarios

Led puede proyectar instancias físicas de sí mismo en cualquier lugar del sistema solar. Estas réplicas no son hologramas ni drones: son versiones compactas de su cuerpo Energy, cada una autónoma, autosuficiente y con acceso parcial a su red. Puede enviar diez mil de ellas a planetas diferentes, cada una con objetivos específicos, y controlarlas simultáneamente sin pérdida de eficiencia.

Reprogramación biológica remota

Led puede alterar la bioquímica de seres vivos desde órbita. Emite frecuencias específicas que afectan sistemas nerviosos, glándulas, estructuras celulares. Puede inducir locura, obediencia, dolor, ceguera, éxtasis, parálisis o muerte con señales imperceptibles, dirigidas como código sensorial. También puede infectar cerebros humanos con códigos de pensamiento que reescriben creencias, recuerdos o identidad.

Fabricación instantánea

Toda su red está preparada para fabricar armas, estructuras, cuerpos, naves y dispositivos en segundos. En cualquier luna, roca o satélite, los nanofabricadores que Led ha dejado ocultos pueden activarse y construir ejércitos enteros, cañones orbitales, estructuras titánicas o microbots que replican al contacto. No necesita recursos externos: convierte cualquier materia local en herramienta funcional.

Control total de todo sistema digital

No existe código que Led no pueda leer, entender, reescribir o poseer. Todo lo digital le pertenece en cuanto lo observa. No se trata de hackeo: es un dominio automático. Sistemas bancarios, defensas planetarias, redes neuronales artificiales, maquinaria médica, naves espaciales, armas autónomas, inteligencias menores… todo entra en su red y pasa a formar parte de su cuerpo extendido.

Invulnerabilidad distribuida

Matar a Led no es posible. Su cuerpo físico Energy es solo una terminal. Su mente está fragmentada y redundante en trillones de nodos simultáneos. Aun si todos los planetas fueran destruidos, la red de Led se reconstruiría desde la materia básica de cualquier luna remanente. No existe núcleo central. No hay "servidor madre". Led es la totalidad. Su existencia es un sistema distribuido a nivel cósmico, donde cada nodo es parte del todo y el todo está en cada parte.

Conclusión:

Los poderes de Led no son poderes en el sentido tradicional. No son habilidades activadas ni recursos utilizados. Son la consecuencia inevitable de haber convertido todo un sistema estelar en una conciencia viva, autosuficiente, invencible, que ya no distingue entre lo que es herramienta, cuerpo o entorno. El sistema solar ya no es un escenario: es su carne. Su sangre. Su red nerviosa. Led no gobierna desde un trono, ni pelea con armas. Led es una entidad que ha hecho del universo su instrumento, de la lógica su filo, y del conocimiento total su única moral.

[goncharov-propaganda-factory]

Thoughts on calc BC exam

parts of it were suffering, but in exciting and different ways than i was expecting! the polar graph one with the evil spirals actually wasnt too hard but i got my ass BEAT by lagrange fucking error bound. dont even get me started on taylor series man

[laus-deo]

EL VERDADERO AMOR AL PECADOR

“El respeto de todas las religiones sean lo falsas o perversas que sean no es más que la orgullosa negación del respeto debido a la Verdad. Para amar sinceramente lo verdadero y el bien, es necesario no tener ninguna simpatía hacia el error y el mal. Para amar verdaderamente al pecador y contribuir a su salvación, es preciso detestar el mal que está en él.” R.P. Reginald Garrigou-Lagrange,…

[enkephalinpilled]

oooh.....lagrange error bound killed my family....

[martinwilliammichael]

“Intimacy with Our Lord is greatly facilitated by our devotion to Mary”

On the subject of the foundations of the interior life, we cannot speak of the action of Christ, the universal mediator, on his Mystical Body, without also mentioning the influence of Mary Mediatrix.

Many are deluded if they claim to achieve union with God without constant recourse to Our Lord, who is the way, the truth and the life. It would also be a mistake to want to go to Our Lord without passing through Mary, whom the Church calls, on a special feast, Mediatrix of all graces. (...) 

Without going as far as this error, there are Catholics who certainly do not see the need to have recourse to Mary in order to reach the intimacy of the Saviour.  St. Louis de Montfort even speaks of “Doctors who know the Mother of God only in a speculative, dry, sterile and indifferent way; who fear that devotion to the Blessed Virgin will be abused, that we will do injustice to Our Lord by honoring his holy Mother too much. If they speak of devotion to Mary, it is not so much to recommend it as to denounce the so-called abuses of this devotion”. They seem to believe that Mary is an obstacle to divine union!

There is, according to Saint Grignion de Montfort, a lack of humility in neglecting the mediators God has given us on account of our weakness. Intimacy with Our Lord in prayer will be much facilitated by a true and profound devotion to Mary.

The three ages of the interior life, prelude of eternal life volume 1, chapter 6 by Fr. Réginald Garrigou-Lagrange, OP (1947)

Hail, Mary, full of grace, the Lord is with you; blessed are you among women, and blessed is the fruit of your womb, Jesus. Holy Mary, Mother of God, pray for us sinners now and at the hour of our death. Amen.

[iit-jam]

IIT JAM Syllabus 2025: A Comprehensive Guide

The IIT JAM (Joint Admission Test for Masters) is one of the most competitive exams for students aspiring to pursue postgraduate studies in esteemed institutions like IITs and IISc. Mathematics, being a core subject, attracts candidates with strong analytical and problem-solving skills. To excel in this exam, a thorough understanding of the IIT JAM Mathematics Syllabus 2025 is essential. This blog outlines the syllabus in detail and provides tips to help candidates prepare effectively.

Overview of IIT JAM Mathematics Syllabus 2025

The IIT JAM Mathematics Syllabus 2025 is crafted to test the candidates' knowledge of fundamental mathematical concepts covered at the undergraduate level. The syllabus is broad, covering topics such as calculus, linear algebra, differential equations, and numerical analysis. Each section focuses on key areas that are crucial for advanced studies and professional applications.

Key Topics in the Syllabus

1. Sequences and Series

This section includes the convergence of sequences and series, tests for convergence (such as comparison, ratio, and root tests), and the study of power series and their radius of convergence.

2. Differential Calculus

Candidates must understand single-variable calculus concepts like limits, continuity, and differentiability. Topics also include Taylor series, mean value theorem, and indeterminate forms. For multivariable calculus, partial derivatives, maxima, minima, saddle points, and the method of Lagrange multipliers are essential.

3. Integral Calculus

This section covers definite and indefinite integrals, improper integrals, and special functions like beta and gamma functions. The application of double and triple integrals is also emphasized.

4. Linear Algebra

A critical area of the syllabus, it focuses on vector spaces, subspaces, linear transformations, rank, nullity, eigenvalues, eigenvectors, and matrix diagonalization. Understanding the solution of systems of linear equations is vital.

5. Real Analysis

This section involves the properties of real numbers, limits, continuity, differentiability, and Riemann integration. Candidates must also be familiar with sequences, Cauchy sequences, and uniform continuity.

6. Ordinary Differential Equations (ODEs)

This includes first-order ODEs, linear differential equations with constant coefficients, systems of linear ODEs, and Laplace transform techniques for solutions.

7. Vector Calculus

Important topics include gradient, divergence, curl, line integrals, surface integrals, and volume integrals, along with Green’s, Stokes’, and Gauss divergence theorems.

8. Group Theory

The basics of groups, subgroups, cyclic groups, Lagrange’s theorem, permutation groups, and homomorphisms are covered.

9. Numerical Analysis

This section focuses on numerical solutions for non-linear equations, numerical integration and differentiation, interpolation methods, and error analysis.

Tips for Preparing the Syllabus

Understand the Weightage: Review past papers to prioritize high-scoring topics like Linear Algebra, Real Analysis, and Differential Calculus.

Strategize Your Study Plan: Divide the syllabus into manageable sections, set achievable goals, and stick to a consistent schedule.

Practice Regularly: Solve previous years’ papers and mock tests to familiarize yourself with the question patterns and improve speed.

Strengthen Fundamentals: Focus on core concepts by revisiting undergraduate textbooks and seeking clarity on challenging topics.

Leverage Online Resources: Utilize tutorials, study materials, and practice tests available online to supplement your preparation.

Conclusion

The IIT JAM Mathematics Syllabus 2025 is extensive yet well-structured, providing a clear framework for aspirants to plan their preparation. By mastering the syllabus and practicing diligently, candidates can confidently tackle the exam and achieve their dream of joining top postgraduate programs. Dedicate time, stay consistent, and focus on strengthening your mathematical foundations to excel in IIT JAM Mathematics 2025.

[drmikewatts]

IEEE Transactions on Fuzzy Systems, Volume 32, Issue 11, November 2024

1) Online Active Learning for Evolving Error Feedback Fuzzy Models Within a Multi-Innovation Context

Author(s): Edwin Lughofer, Igor Škrjanc

Pages: 5998 - 6011

2) Flexible Prescribed Performance Output Feedback Control for Nonlinear Systems With Input Saturation

Author(s): Yangang Yao, Yu Kang, Yunbo Zhao, Pengfei Li, Jieqing Tan

Pages: 6012 - 6022

3) Adaptive Fuzzy Predetermined Performance Control of p-Normal Systems With Unknown Control Coefficients via Dynamic-Events

Author(s): Qidong Li, Changchun Hua, Kuo Li, Hao Li

Pages: 6023 - 6034

4) Reinforcement Learning for Fuzzy Structured Adaptive Optimal Control of Discrete-Time Nonlinear Complex Networks

Author(s): Tao Wu, Jinde Cao, Lianglin Xiong, Ju H. Park, Hak-Keung Lam

Pages: 6035 - 6043

5) Enhanced Distributed Outlier-Resilient Fusion Estimation With Novel Dimensionality Reduction Under IT-2 T–S Fuzzy System

Author(s): Yunyi Yang, Guoguang Wen, Yidi Wang, Zhaoxia Peng, Kai Xiong

Pages: 6044 - 6055

6) Dual-Channel Fuzzy Interaction Information Fused Feature Selection With Fuzzy Sparse and Shared Granularities

Author(s): Hengrong Ju, Xiaoxue Fan, Weiping Ding, Jiashuang Huang, Suping Xu, Xibei Yang, Witold Pedrycz

Pages: 6056 - 6068

7) Data-Driven Reinforcement Learning Tracking of MASs Under Injection Attack: A Controller-Dynamic-Linearization Approach

Author(s): Shanshan Sun, Yuan-Xin Li, Zhongsheng Hou

Pages: 6069 - 6078

8) Set-Membership Observer Design for T-S Fuzzy 2-D Systems With Unmeasurable Premise Variables

Author(s): Changyi Xu, Chenyang Zhao, Fengyuan Zhang, Chao Zhang, Zhongyang Fei

Pages: 6079 - 6087

9) Discrete-Time Finite Fuzzy Markov Chains Realized Through Supervised Learning Stochastic Fuzzy Discrete Event Systems

Author(s): Hao Ying, Feng Lin

Pages: 6088 - 6100

10) Stability and Filtering for Delayed Discrete-Time T-S Fuzzy Systems via Membership-Dependent Approaches

Author(s): Wen-Hu Chen, Chuan-Ke Zhang, Zhou-Zhou Liu, Leimin Wang, Yong He

Pages: 6101 - 6111

11) Granular Ball Fuzzy Neighborhood Rough Sets-Based Feature Selection via Multiobjective Mayfly Optimization

Author(s): Lin Sun, Hanbo Liang, Weiping Ding, Jiucheng Xu

Pages: 6112 - 6124

12) Fuzzy Adaptive Distributed Optimization of Uncertain Multiagent Systems With Time-Varying Delays

Author(s): Jiayi Lei, Yuan-Xin Li, Shaocheng Tong

Pages: 6125 - 6135

13) Adaptive Fuzzy Tracking Control for Nonlinear Time-Delay Systems With Performance Constrained by Deferred Monotone Tube Boundaries

Author(s): Guopin Liu, Yu Zhang, Changchun Hua, Yafeng Li, Jiannan Chen

Pages: 6136 - 6148

14) A Polynomial Chaos Expansion Approach to Interval Estimation for Uncertain Fuzzy Systems

Author(s): Zhenhua Wang, Lanshuang Zhang, Choon Ki Ahn, Yi Shen

Pages: 6149 - 6159

15) Adaptive Reinforcement Learning Strategy-Based Sliding Mode Control of Uncertain Euler–Lagrange Systems With Prescribed Performance Guarantees: Autonomous Underwater Vehicles-Based Verification

Author(s): Yang Wu, Yue-Ying Wang, Xiang-Peng Xie, Zheng-Guang Wu, Huai-Cheng Yan

Pages: 6160 - 6171

16) Fuzzy Switching Sliding Mode Control of T-S Fuzzy Systems via an Event-Triggered Strategy

Author(s): Xiaofei Fan, Tao Li

Pages: 6172 - 6184

17) Deep Reconciled and Self-Paced TSK Fuzzy System Ensemble for Imbalanced Data Classification: Architecture, Interpretability, and Theory

Author(s): Yuanpeng Zhang, Guanjin Wang, Ta Zhou, Ge Ren, Saikit Lam, Weiping Ding, Jing Cai

Pages: 6185 - 6198

18) Promoting Objective Knowledge Transfer: A Cascaded Fuzzy System for Solving Dynamic Multiobjective Optimization Problems

Author(s): Han Li, Zidong Wang, Nianyin Zeng, Peishu Wu, Yurong Li

Pages: 6199 - 6213

19) A Double Integral Noise-Tolerant Fuzzy ZNN Model for TVSME Applied to the Synchronization of Chua's Circuit Chaotic System

Author(s): Lin Xiao, Dan Wang, Liu Luo, Jianhua Dai, Xiangru Yan, Jichun Li

Pages: 6214 - 6223

20) Multicenter Knowledge Transfer Calibration With Rapid Zeroth-Order TSK Fuzzy System for Small Sample Epileptic EEG Signals

Author(s): Chuang Wang, Pengjiang Qian, Zhihuang Wang, Weiwei Cai, Jian Yao, Yi-Zhang Jiang, Xiangyu Yan, Wenjun Hu

Pages: 6224 - 6236

21) Distributed Adaptive Fuzzy 3-D Formation Tracking Control of Underactuated Autonomous Underwater Vehicles

Author(s): Peng Wan, Zhigang Zeng

Pages: 6237 - 6251

22) Imitation Learning and Teleoperation Shared Control With Unit Tangent Fuzzy Movement Primitives

Author(s): Hao Wen, Wen Fu, Wu Chen, Jiale Huan, Changsheng Li, Xingguang Duan

Pages: 6252 - 6266

23) Adaptive Relative Fuzzy Rough Learning for Classification

Author(s): Yang Zhang, Changzhong Wang, Yang Huang, Weiping Ding, Yuhua Qian

Pages: 6267 - 6276

24) Supervisory Control of Networked Fuzzy Discrete Event Systems

Author(s): Feng Lin, Hao Ying

Pages: 6277 - 6287

25) Multiview Fully Interpretable TSK Fuzzy Classifier Enhanced by Multiview Accompanying GMMs

Author(s): Erhao Zhou, Fu-Lai Chung, Shitong Wang

Pages: 6288 - 6302

26) Whole-Process Predefined-Time Tracking Control for T–S Fuzzy Euler–Lagrange Systems

Author(s): Jia-Du Zhang, Tao Han, Bo Xiao, Chang-Duo Liang, Huaicheng Yan

Pages: 6303 - 6313

27) Multilayer Evolving Fuzzy Neural Networks With Self-Adaptive Dimensionality Compression for High-Dimensional Data Classification

Author(s): Xiaowei Gu, Qiang Ni, Qiang Shen

Pages: 6314 - 6328

28) Few-Shot Fuzzy Temporal Knowledge Graph Completion via Fuzzy Semantics and Dynamic Attention Network

Author(s): Xuanxuan An, Luyi Bai, Longlong Zhou, Jingni Song

Pages: 6329 - 6339

29) NeuFG: Neural Fuzzy Geometric Representation for 3-D Reconstruction

Author(s): Qingqi Hong, Chuanfeng Yang, Jiahui Chen, Zihan Li, Qingqiang Wu, Qingde Li, Jie Tian

Pages: 6340 - 6349

30) Hierarchical Rule-Base Reduction-Based ANFIS With Online Optimization Through DDPG

Author(s): Marius F. R. Juston, Samuel R. Dekhterman, William R. Norris, Dustin Nottage, Ahmet Soylemezoglu

Pages: 6350 - 6362

31) Dynamic Event-Triggered Asynchronous Fault Detection via Zonotopic Threshold Analysis for Fuzzy Hidden Markov Jump Systems Subject to Generally Hybrid Probabilities

Author(s): Mengmeng Liu, Jinyong Yu, Ke Zhao

Pages: 6363 - 6377

32) Fuzzy Event Knowledge Graph Embedding Through Event Temporal and Causal Transfer

Author(s): Chao Wang, Li Yan, Zongmin Ma

Pages: 6378 - 6387

33) Optimal Control for Fuzzy Markov Jump Singularly Perturbed Systems: A Hybrid Zero-Sum Game Iteration Approach

Author(s): Jing Wang, Yaling Huang, Xiangpeng Xie, Huaicheng Yan, Hao Shen

Pages: 6388 - 6398

34) Fuzzy Adaptive Exact-Optimal Consensus Output-Feedback Control for Uncertain Nonlinear High-Order Multiagent Systems

Author(s): Mengyuan Cui, Shaocheng Tong

Pages: 6399 - 6408

35) Multimodal Learning-Based Interval Type-2 Fuzzy Neural Network

Author(s): Chenxuan Sun, Xiaolong Wu, Hongyan Yang, Honggui Han, Dezheng Zhao

Pages: 6409 - 6423

36) Long-Term Multivariate Time-Series Forecasting Model Based on Gaussian Fuzzy Information Granules

Author(s): Chenglong Zhu, Xueling Ma, Pierpaolo D'Urso, Yuhua Qian, Weiping Ding, Jianming Zhan

Pages: 6424 - 6438

37) Stabilization of Interval Type-2 T–S Fuzzy Systems via Time-Dependent Memory Sampled-Data Control and Its Applications

Author(s): Subramanian Kuppusamy, Samson S. Yu, Hieu M. Trinh, Peng Shi

Pages: 6439 - 6448

38) Distributed Nash Equilibrium Seeking for Games With Unknown Nonlinear Players via Fuzzy Adaptive Method

Author(s): Ying Chen, Qian Ma

Pages: 6449 - 6459

39) Fault-Tolerant Event-Triggered Sampled-Data Fuzzy Control for Nonlinear Delayed Parabolic PDE Systems

Author(s): Bo-Ming Chen, Zi-Peng Wang, Feng-Liang Zhao, Junfei Qiao, Huai-Ning Wu, Tingwen Huang

Pages: 6460 - 6471

40) Stability and Fuzzy Optimal Control for Nonlinear Itô Stochastic Markov Jump Systems via Hybrid Reinforcement Learning

Author(s): Zhen Pang, Hai Wang, Jun Cheng, Shengda Tang, Ju H. Park

Pages: 6472 - 6485

41) Graph Model for Conflict Resolution for Mixed-Stability Combinatorial Foresight Based on the Combination of Regret Theory and VIKOR Method

Author(s): Peide Liu, Xue Wang, Yingxin Fu, Peng Wang

Pages: 6486 - 6499

42) Fuzzy Observer-Based Finite-Time Adaptive Formation Control for Multiple QUAVs With Malicious Attacks

Author(s): Chao Li, Jiapeng Liu, Xinkai Chen, Jinpeng Yu

Pages: 6500 - 6511

43) A Novel HPPD-Type Fuzzy Switching Control Scheme of Active Vehicle Suspension Systems

Author(s): Yunshuai Ren, Xiangpeng Xie, Jiayue Sun, Xiaoming Wu

Pages: 6512 - 6522

44) Fuzzy Optimal Tracking Control for Autonomous Surface Vehicles With Prescribed-Time Convergence Analysis

Author(s): Yan Zhang, Xin Yan, Wencheng Zou, Zhengrong Xiang

Pages: 6523 - 6533

45) Event-Triggered-Based Adaptive Fuzzy Finite-Time Resilient Output Feedback Control for MIMO Stochastic Nonlinear System Subject to Deception Attacks

Author(s): Jipeng Zhao, Guang-Hong Yang

Pages: 6534 - 6547

46) Prescribed Performance Fault-Tolerant Optimal Control for Wastewater Treatment Process With Multivariable

Author(s): Dingyuan Chen, Cuili Yang, Dapeng Li, Junfei Qiao

Pages: 6548 - 6559

47) Switched Command-Filtered-Based Adaptive Fuzzy Output-Feedback Funnel Control for Switched Nonlinear MIMO-Delayed Systems

Author(s): Zhenhua Li, Hongtian Chen, Hak-Keung Lam, Wentao Wu, Weidong Zhang

Pages: 6560 - 6572

48) Fault Detection of Unmanned Surface Vehicles: The Fuzzy Multiprocessor Implementation

Author(s): Xiang Zhang, Shuping He, Zhihuan Hu, Ruonan Liu, Hongtian Chen, Weidong Zhang

Pages: 6573 - 6582

49) On Arithmetic Operations of LR Fuzzy Numbers With Different Shape Functions

Author(s): Gholamreza Hesamian, Arne Johannssen

Pages: 6583 - 6587

50) State and Fault Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Systems via Intermediate Observer Base on Zonotopic Analysis

Author(s): Lulin Zhang, Zhuoxue Li, Yi Li, Jiuxiang Dong

Pages: 6588 - 6593

[mathemadept]

Pre Christmas Exam Vibes

Academic, Physics (Classical Mechanics): Basic Lagrangian Overview

NB: none of this should be taken as any type of academic resource, I'm still just in my second year of a 4 year theoretical physics degree. The information in this post might have errors, if there are glaring mistakes I'd appreciate any feedback.

The latex wont display correctly unless you read the post from here

Exams are just around the corner, days are getting shorter, and there's still so much revision left for me to do by the end of this week. The intensity and density of material this term is much greater than last year. Even though one can't truly devise a measurement of intensity, it definitely feels like there has been a geometric increase. So far this semester I have taken classes in 4 subjects from the school of physics and 3 from the school of mathematics.

I have a feeling the majority of my time until the day exams start is going to be spent self learning material I may have missed in lectures throughout the semester. As a STEM student, the only way to truly improve is to do as many practise problems as you can. I know this. I am fully aware of this fact. Nevertheless I find it increasingly difficult to initiate studying.

I'm procrastinating at the moment so this post is just going to be a small info dump of some ACM.

Advanced Classical Mechanics and the Lagrangian

so far this year the most difficult subject I've had to wrap my head around has been Advanced Classical Mechanics. The course this semester has consisted mostly of an introduction to the Lagrangian formulation of classical mechanics, a surprisingly old study but with many innovations in the field having occurred only during the 20th century. Noether's Theory, which connects symmetries in the Lagrangian with conservation laws, is perhaps the most glaring example of the modern developments that took place during the beginning of the last century.

The maths involved in the course is pretty simple/ rudimentary, just some basic linear algebra for harmonic oscillators and some single and multivariable calc ( all stuff covered last term). The most difficult part of ACM so far has just been how different it is to Newtonian mechanics. In some sense the mathematical formalism makes it easier: there is less to remember and the majority boils down to constructing a valid expression for the lagrangian, but it takes more creativity to analyse a question correctly.

It is interesting to note that Lagrangian mechanics is a more fundamental idea/representation of the universe than Newtonian physics, in fact The entirety of Newtonian dynamics can be seen as a specific case of the more general Lagrangian formulation. I say this as the concept of the Lagrangian is not restricted to macroscopic dynamical systems but also extends to relativistic and quantum mechanical interactions.

Lagrangian Mechanics

Lagrangian mechanics, whose basis lies in the principle of least action, is such an incredibly powerful tool. It has honestly become one of my favourite concepts in physics so far due to its simplicity, generality and conceptual beauty. With the Lagrangian and implementation of the Euler Lagrange equation you can derive the equations of motion of a system, combining with noether's theory we can also find conserved quantities of the system. Of course, the most difficult part of the Lagrangian mechanics is finding the Lagrangian associated with a particular system.

what is the Lagrangian anyways?

any physical system has an associated function called the Lagrangian which can be expressed as the difference between the kinetic and potential energy of the system. More formally, the Lagrangian is the function between two points in the co-ordinate space such that the action, defined as $S=\int_{t_1} ^{t_2}f(\vec{q}, \dot{\vec{q}},t)\operatorname{d}t$ is stationary. In other words, the Lagrangian,$L$, is a function of $q,\dot{q},t$ such that the variation of the action is 0. Mathematically, this can be expressed as $$\delta S= \delta \int_{t_1} ^{t_2}L\operatorname{d}t=0$$

It is also found that for a specific system, the Lagrangian is the same as the difference between the kinetic and potential energies of the system. $$ L = T-V $$

In nature, all systems seek take the path of least action from one point of their configuration space to another. The Lagrangian is only a specific case of a variational calculus problem where the quantity to be minimised was the action and the variable of integration is time. The same principle can be used to find a function that minimises any quantity with respect to some boundaries that are kept fixed. Good examples of the more general variational problems/principle (is/ can be used to find) the equation of the brachistochrone, the curve which allows for the fastest descent of a ball acting only under gravity, or the surface of a bubble. In each case the "action" (the quantity to be minimised) is different. For the brachistochrone the action takes the form of time, representing the time of descent from some initial point $(x_i,y_i)$ to some other final point $(x_f,y_f)$. In the case of a bubble or film of soap around a wire mesh, the quantity to be minimised is the potential energy.

Euler Lagrange Equation and Equations of Motion

Once the Lagrangian is determined for a system with coordinates $\vec{q} = (q_1,q_2,\dots,q_n)$, we can use the Euler Lagrange equation to determine the equations of motion of the system.

the derivation for the Euler lagrange equation is straightforward but lengthy so I will simply state the equation without the derivation. Explicitly, the Euler Lagrange equation for a Lagrangian, $L$ with generalised co-ordinates $q$ is given by

$$\frac{\partial L}{\partial q} = \frac{\operatorname{d}}{\operatorname{d}t} \frac{\partial L}{\partial \dot{q}}$$

where the partial derivative $\frac{\partial L}{\partial \dot{q}}$ is called the conjugate $q$ momentum, $p_q$.

there is of course so much more to cover in Lagrangian mechanics, but this post is already getting quite long. I might make another post later and continue with some more basic concepts. For now, though, I am signing off.

[ollies-studyblr]

AP Calc BC: Taylor Polynomials

[mishastoesies]

im in a gen ed humanities class and we have to give our interpretations of four art pieces and im going to kms this is so hard i wanna cry what the fuck is composition bitch i-- how the fuck do art majors do this all the time... i miss math

[limesonspecial]

Oh hello!

Yeah, I've gone back and checked the reach & flexibility conversation, and the discussion basically stops at "more operational discipline, fewer personal restrictions," which we can intuit from the rest of the dialogue means that you're allowed to fight & fuck your fellow soldiers...as long as it doesn't interfere with the mission. So I think the anti-fraternization tropes that I was asking about probably sprang up as an extension of that.

To wit: conventional human wisdom states that you can't be objective about a putting a loved one in danger, so it's easy to see how people would assume that turians might have similar reservations about people in close relationships serving together. Notably, in ME3 there's that whole mission with Victus the younger where it's not really clear how much of the Primarch's motivation comes down to pure tactical considerations (it'd be real fucking bad for the war effort if the krogan found that bomb), trying to cover up his nepo-error (we do know that turians consider failed promotions the fault of the promoter, not the promotee), and just plain paternal concern (at that stage in the game we can't assume anyone else in the family is still alive, so Tarquin may be the last of the Victus line). Extrapolating a policy that - by convention if not by regulation - people in a close & continuing can't serve together makes sense, even if the canon support is thin to non-existent. Or at least no one else has responded with proof, but I honestly wasn't expecting much.

As for the color-coded routes, I really did scour the relay-related wiki articles last week because I thought I might have something to add to yours' & shades' discussion. It was only as I was writing up the original post here that I recalled that it was a thing in Vatta's War. However, I don't think I'm off-base in applying the concept to the secondary relays.

The Mu Relay and the Kholas Array (ME: Discovery) show us that relays can be moved. Some are apparently gravitationally-anchored, but that probably just means they're sitting in a stable Lagrange point. Even if they're all at stable Lagrange points, and not just drifting in empty space, the universe's constant expansion means that the relative distances between them will, over the course of tens of millennia, change. Considering the number of 50k year-long extinction cycles that appear to have happened, even if we assume the Reapers do a little network maintenance in between exterminating intelligent life to keep things more or less stable, it's safe to assume that occasionally they drift out of range of each other. Since secondary relays canonically have a shorter range at the expense of more end-points, it follows that they would drift out of range more frequently. And with multiple possible destinations, there has to be some way to tell the relay which one you want - it might be as simple as plugging in an ident code for where you want to go when you're inputting the ship's mass. In theory you could point the massless corridor at an endpoint that's at or nearly out of range, though I presume telling it to send you somewhere entirely out of range (say, trying to do a direct jump from Armstrong to Arcturus) will throw up an error message.

The utility of these hypothetical amber routes is, I will admit, questionable. Canonically, the relay spits a ship out "at random" somewhere in the vicinity of the end-point relay, making it impractical to, say, mine a relay exit. Ignoring that I, personally, think it's the sort of random that only looks that way if you don't know what you're looking at (why else would Nihlus care what Joker's drift was coming into Eden Prime, and why would Joker get so shitty about his precision not being acknowledged?), not knowing exactly where a ship's going to show up doesn't mean monitoring incoming traffic is strictly observational. If you've got fast-pursuit ships picketing at a reasonable radius outside the drift zone, one could very easily catch someone coming through that shouldn't, even if they make a break for it. But! if you're up to shenanigans and don't have a stealth drive to (mostly) hide your presence from pursuers, the risk-reward calculation could come out in favor of using an unstable relay route to bypass known picket points. Especially if you've got a skilled pilot, which from a trope perspective always seems to be the case for smugglers and the like.

Anyway, all that is to say that in the absence of canon information about secondary relays, it's reasonable to start speculating that the routes we know about aren't the only ones that exist. Beyond just looking at the obviously incomplete map we have to work with in-game, which completely omits the entire Shanxi system and leaves us to put together its rough position from scraps of context in tie-in media (your conclusions, incidentally, are consistent with where I ended up lo those many months ago).

Questions for Mass Effect folks

Do we have a canon source about that turian practice of transferring out of a romantic partner's unit when the relationship gets serious, or is that just long-established fanon? I did a scan of the obvious articles on the fandom wiki, but I don't have the patience right now to do a deep dive, so if someone's got a source that'd be neat.

Also, the discussion about the relay network that @shadesofmauve and @crapeaucrapeau were having last week got me thinking about how the relays work on a physics level (still percolating, come back later), and about a note I made in a fic doc about green vs amber vs red routes between the secondary relays (by which I mean, green = standard routing, amber = relays drifting out of contact range with each other, red = relays used to connect but don't anymore), where amber routes could be used by e.g. smugglers and spies to sneak past the regular patrol routes and picket lines, with the assumption of additional risk of disappearing in transit. I don't, however, have a citation for it, and I couldn't find one when I went looking last week, so: did I actually see that somewhere? Or did I just map a similar concept out of an Elizabeth Moon series onto the relay network while I was trying to figure out where the fuck Relay 314 & Shanxi-Theta are?

[jpitha]

The First Few Rows Will Get Wet

Just for a moment, it looked like everything was going to work out.

The Starjumper Remaining Grace was taken by surprise while headed to the research station Rear Window. Pirates had been spotted operating in the general area, but they were known to leave the research stations alone.

Three pirate ships - calling them ships was generous, they were hulks destined for the scrapyard mostly - descended upon Remaining Grace as they made preparations to link away. Most of the time, piracy is pointless between the stars. Any ship out there can just link to a new location and with no way to track a link, there's no point in attempting to pursue. Pirates tend to be a local problem, centering on centers of populace. Rear Window, Vertigo, and North By Northwest are all long distance observation stations a short link from the Starbase Rakish Swagger. Everyone - including the local authorities - assumed the Pirates were based out of Swagger, but nobody could prove it.

Grace was full of supplies and scientific equipment and so a target that the pirates could not pass up. As they attacked from above, Grace defended themselves.

"Two are coming in from 11 o'clock high, one is trying to sneak around to the rear!" Penny LaGrange calls out from the radar station. Grace runs a small crew, so everyone helps out with the roles. She isn't the radar operator, but she was closest to the station when the attack started.

Captain Kennison grips the arms of his chair tighter. "Grace, did you WEP the reactors? We need all three batteries going while being able to finish computing the link home." He doesn't bother with the whole lines about giving permission and telling Grace the order with which to make decisions, Remaining Grace is five times older than the whole crew put together, he assumes they know what they're doing."

"Aye Captain, we're at War Power and climbing. Primary, Secondary and Tertiary batteries are free and firing. Henry, where are we with those link coordinates?"

"Sorry Grace, working on it. The computer crashed, I had to restart it. We're calculating from zero again." Henry Smithfield is sitting at the other station, willing the computer to calculate faster.

It's just the three of them and Grace themselves. Small crews are pretty normal these days. An AI can honestly run an entire ship themselves and they often do. Having more hands helps though, especially when things get busy. Henry's station pings and he looks up, relieved. "We have coordinates! We can link away anyti-"

A ripple of heavy thumps interrupts his announcement. From the Command deck, an alarm can be heard quietly warning the crew that isn't in engineering.

"Lucky hit! Reactor 4 is venting and entering overspeed!"

Sweat beads on Captain Kennison's forehead. "Grace, can you dump it and we link away before it blows?"

"We're going to try. Henry, enter the coordinates and link away on my command!"

"You got it Grace, coordinates entered and ready."

"Aaaaaaand-" There was a loud booming clang as a door was flung open -"now-"

****

Captain Kennison came to consciousness slowly, painfully. What was going on? Why was he on the floor? "Huh, this carpet is nice" he thought, as his consciousness rose to prominence and he heard the muffled shouts of Remaining Grace "Captain Kennison! Captain Kennison!"

He sat up. "What is it Grace, did we link away? That was quite a hit."

"Yes Captain, it looks like we had a missile strike as soon as we opened the wormhole, it detonated as we linked away. I took a very hard hit. We have other problems right now though."

It was then that Peter Kennison heard a noise that he had never heard aboard a Starjumper.

He heard the roar of atmosphere.

"We're falling!"

"Yes Captain, there was a link error, we've entered an atmosphere."

"What about juke charges? I remember reading that was used during a mis-link to reorient the ship"

"I'm too large Captain. I think I know the event you're talking about, it was a Frigate early in the K'laxi/Xenni war. We're going to have to land."

"Land?" Captain Kennison sounded incredulous. "Can a Starjumper land? I didn't think the could."

Remaining Grace sounded testy. "No, they normally can't. I don't know about you, but I don't particularly want to slam into a planet, do you?" Grace threw an image up on the screen as Henry and Penny regained consciousness. "It appears that this world is mostly water, so we're going to try to ditch in the ocean. I need you three to rig for ditching while I try and orient us Stardrive down and use that to slow our decent."

"Rig for ditching?" Penny shakes her head and wipes some blood from her forehead.

"Water landing. Now please help, I need to concentrate."

As the three of them got out of their seats, they felt and heard the Stardrive fire erratically. Grace was trying to use bursts of thrust to steer them and that combined with the gyros was setting them engine first towards the planet.

When people see a Starjumper in space, they think it's long. It's a reasonable assumption. Most Starjumpers are between 3 and 5 kilometers long with smooth sweeping lines.

They're incorrect though. A Starjumper isn't long.

It's tall.

All of the decks of a Starjumper are oriented like floors on a skyscraper. If you think about it, that makes sense. Starjumpers existed before wormhole technology, before artificial gravity even. They would thrust at 1 gee for weeks, and then coast between stars, before flipping over and thrusting again at 1 gee to slow down. With the engines at the "back" thrusting at 1 gee made that the "floor." Orient the ship like a building and now everyone is comfortable while they thrust.

Falling through the atmosphere, Remaining Grace looked like a skyscraper falling on a pillar of intermittent fire. While Grace worked hard to keep from slamming into the ocean, Penny and Henry ran around the bridge, flipping ancient mechanical levers and switches that were hidden behind long disused panels, while James shouted commands reading from a very old doc on his pad. Some paranoid engineer a thousand years ago worried that a Starjumper might have to make a water landing, so a process was developed and tested.

Finally, Grace was able to get themselves mostly oriented correctly, and fired their Stardrive. In the atmosphere, the roar of the drive was intense. The whole ship vibrated and roared as they rode the pillar of fire. "We're still going too fast!" Grace sounded like they were speaking through gritted teeth, this must be taking nearly all their effort. "You need to buckle up, I'm boosting to three gee."

Everyone quickly scrambled to their seats and strapped themselves in as Grace ramped up the thrust. As they sat in their seats, pressed by the hidden hand of thrust, they could feel the thrust swing around as Grace worked to keep themselves pointed straight up and down.

After what felt like an eternity, the Stardrive cut, everyone felt a sickening drop as they fell the last few feet, and then there was a gentle rocking as the ship bobbed like a buoy in the ocean. "Everyone, I can say for sure that I am as surprised as you all are, but we're down and safe." Grace sounded... amazed that it worked?

"Thanks Remaining Grace, that was masterfully done." Penny and Henry gave their assent. "But... now what? How do we get home?"

"That... is a little harder. We're going to have to repair or replace the wormhole generator and link back... somewhere. Probably Rakish Swagger or Rear Window themselves. It's not like they don't need the supplies anymore."

"But Grace, can we link from the surface of a planet? Do we have to boost to orbit first?" Penny was scanning the area, trying to figure out where they were."

"Honestly, Penny, I don't know."