Study of Linear and Nonlinear Models with “Mathematca”

Czesław Mączka

AGH University of Science and Technology, Poland

Sergii Skuratvskyi

Natonal Academy of Science of Ukraine, Ukraine

Key Features

Vsevolod Vladimirov

AGH University of Science and Technology, Poland

• Educatonal material or a ull two semester course has been collected. he presentaton is carried out according to the principle o transiton rom simple to comple , there ore the frst part covering one semester course is entrel based on the classical material including various aspects o nonlinear mechanics and the theor o oscillatons, while the second part, devoted to modeling ph sical felds, combines classical sectons with material re ectng modern aspects o research

• he book includes an e tensive secton devoted to linear models o mathematcal ph sics and methods or their solutons. rom the point o view o the advantages provided b the use o so ware packages such as athematca , linear models represent the most ertle feld or applicaton, because the solve, as a rule, in a ma er o seconds those problem that, being calculated manuall , take a lot o tme and re uire signifcant de terit

• he book contains various applicatons o the classical Hirota method, known rom theor o solitons, or obtaining e act solutons to a large number o nonlinear models in no wa related to soliton topics

• Progress in the wide and success ul applicaton o the Hirota method and its modifcatons was due precisel to the possibilit o using special so ware packages, as this is illustrated in the relevant sectons. he methods presented, as well as the corresponding programs, can be easil adapted to solve the problems o this kind that are o interest to a potental reader

• he authors paid special a enton to balancing the levels o ph sical and mathematcal presentaton o the material so that the book be understandable to the widest possible range o readers background

• he book combines well known acts and the recent research, which helps lecturers to present modern achievements o nonlinear science, and students to get an idea o the actual work o scientsts

• ogether with the book, computer programs are provided, which not onl visuali e the material o the book, but can also be the basis or students to develop and anal e their own models

• he e amples discussed in the book are multdisciplinar , which makes the manuscript interestng or a wide audience

• he book presents a number o new results o the authors, in partcular, the search or e act solutons o urgers t pe e uatons, the stud o the structure o non anal tcal solutons o evoluton e uatons, the constructon o e act sel similar solutons to various nonlinear models. Special a enton is paid to the stud o locali ed wave modes (solitons, compactons), their ormaton and evoluton within the models taking into account propertes o the carrier medium, such as the osenau H man K(m, n) hierarch , esterenko s e uaton and h drod namic t pe model o rela ing media. t is important that the book collects in one place the mentoned nonlinear models and describes in detail the numerical schemes, which are sca ered among the various scientfc papers

Descripton

The book is devoted to the problems of modeling physical systems and felds using the tools and capabilites of the “Mathematca” sofware package. n the process o teaching classical courses in mechanics and mathematcal ph sics, one o en has to overcome signifcant di cultes associated with the cumbersomeness o the mathematcal apparatus, which more than once distracts rom the essence o the problems under consideraton. he use o the athematca package, which has a rich set o anal tcal and graphic tools, makes the presentaton o classic issues related to modeling and interpretaton o ph sical processes much more transparent. his package enables the visuali aton o both anal tcal solutons o nonlinear di erental e uatons and solutons obtained in the orm o infnite series or special unctons.

January 2023

Imprint: World Scientfc Publishing Compan

Extent: 332pp

Type: e tbook

Main Subject: athematcs

Sub-Subjects: Classical echanics echanics Partcles nd S stems namical S stems nd Ergodic heor General pplied athematcs athematcal odeling onlinear Science, Chaos namical S stems nterdisciplinar Ph sics Computatonal, athematcal nd heoretcal Ph sics So ware Engineering Programming

Keywords: ndronov Hop i urcaton uckingham s Pi heorem Cole Hop rans ormaton Hirota ethod Lagrange s ormalism Hamiltonian S stem Sturm Liouville Problem Completel ntegrable E uaton Central ani old Cascade o Period oubling i urcatons Chaotc Soluton

Readership: Graduate students and researchers interested in mathematcal modeling o nonlinear s stems advanced undergraduate and graduate students in applied mathematcs, ph sics, engineering and technolog researchers in nonlinear science, engineering and technolog libraries

• Models Described in Terms of Ordinary Diferental Equatons and Their Discrete Analogs: Examples of Models Described in Terms of Ordinary Diferental Equatons. Lagrange’s Formalism and Its Applicatons Qualitatve Methods in the Study of Dynamical Systems Models Describing Nonlinear Oscillatons

Oscillatons in Non-Autonomous and Multdimensional Systems

• Models Described in Terms of Partal Diferental Equaton: Models Based on the Concept of Fields Methods of Solving Linear Partal Diferental Equatons Finite-Diference Methods

Some Completely Integrable Nonlinear Models

Techniques and Methods for Obtaining Exact Solutons of Nonlinear Evolutonary Equatons

Nonlinear Wave Paterns Described by Some Non-Integrable Models

• Appendices:

Elements o Calculus o unctons o Comple ariables

Certain Statements ust ing the Use o ntegral rans ormatons n ntroducton into the heor o Special unctons

Shoulder Surgery Made Easy!

The Singapore Shoulder & Elbow Society Guide to Arthroscopic and Open Shoulder Procedures

Denny T T Lie Singapore General Hospital, Singapore

Key Features

• Well proven surgical techni ues developed over 5 ears in one o sia s busiest hospitals ll techni ues are substantated b published clinical results

• Ke acts are summari ed, techni ues wri en in succinct and simple language, presented in point orm or eas reading

• ichl illustrated with more than 280 surgical pictures, diagrams and ow charts

• Comprehensive approach to common shoulder problems, beginning with a diagnostc approach and ph sical e aminaton in chapter , ollowed b imaging o the shoulder (chapter 2) and then pre surgical preparatons in chapter 3

• 9 chapters are dedicated to describing more than 22 surgical procedures each chapter beginning with surgical indicatons, techni ues, post op care and outcomes

• frst or Singapore medicine frst shoulder surgical te tbook b members o the Singapore Shoulder Elbow Societ

• wide potental market in neighbouring countries where Singapore surgeons and members o SSES o en teach

Descripton

What is causing the shoulder pain? How does one prepare or arthroscopic shoulder surger What is ade uate subacromial decompression How does one stabili e the la capsule in the sian shoulder Which o the man suture confguratons should one use or the man tear morphologies his shoulder arthroscopic surger guide a empts to answer the uestons above, and was wri en as a uick re erence and guide or rthopaedic residents and practcing surgeons, with proven techni ues developed b the author and contributors over the past 5 ears. Each surgical techni ue has proven published results and thus provides an assurance to the readers that these techni ues are reproducible. he book starts with a chapter dedicated to a diagnostc approach to shoulder problems, o en a con using s mptom that is not well studied. ore than 22 surgical techni ues are described in detail, in succinct and simple point orms, each chapter beginning with an introducton to the problem, the surgical techni ue which the author(s) ound use ul, post op care and ending o with the clinical results o this techni ue. his 240 page book is illustrated with about 280 pictures and drawings.

Shoulder surger , especiall arthroscopic procedures, have seen a dramatc increase in the past 0 ears. With improved diagnostc modalites, increased awareness and rapid advances in implant technologies, the minimall invasive surgical opton has been more appealing to patents.

Author

A/Prof Denny Lie is a Senior Consultant rthopaedic surgeon, practsing at the Singapore General Hospital, in the feld o shoulder and sports surger . He has per ormed about 2000 shoulder surgeries in his 5 ears o post ellowship practce, and teaches medical students rom uke US, LL US and LKC medical schools. He has published more than 80 papers in peer reviewed ournals, and given more than 200 talks in regional and internatonal meetngs. He regularl conducts arthroscop training courses in Singapore and the region. He ounded the Singapore Shoulder Elbow Societ in 20 7 and is currentl the President o the Singapore rthopaedic ssociaton. n additon to being the atonal elegate to the sian Shoulder ssociaton, and other regional associatons, he is a member o the S K S Shoulder Commi ee.

January 2023

Imprint: World Scientfc Publishing

Compan

Extent: 250pp

Type: edical Handbook

Main Subject: edicine

Sub-Subjects: rthopaedics (+Plastc Surger ) iomechanics Surger mSingapore Collecton Southeast sia

Keywords: Shoulder Surgical Guide rthroscop Cu ears ual ow epairs Suture Confguratons argin Convergence Partal ears assive ears Superior Capsular econstructon endon rans er alloon nspace ankart epair Capsular Shi Glenoid one Loss on ankart Glenoid econstructon Latarget emplissage

Readership: Primar market rthopaedic residents and practcing rthopaedic surgeons in Singapore and regional countries in sia especiall ndia and China. Use ul or higher post grad rthopaedic e ams, and could serve as te t guides in shoulder arthroscop courses. Secondar markets dvanced medical undergraduate, post graduate allied healthcare sta , and researchers interested in shoulder surger . his book would also be o interest to implant industr managers in their educatonal and marketng e orts

• pproach to S mptomolog and Ph sical E am o the Shoulder, the iagnostc pproach

• maging o the Shoulder

• Positoning o the Patent, Portals, and ther Preparatons

• ormal Shoulder he Glenohumeral and Subacromial outne

• elease o ro en Shoulder, pproach to St Shoulder with Cu ear

• Labral epair + Capsular Shi

• inor one Loss n pproach, the emplissage Procedure

• a or one Loss ealing with the on ankart, Glenoid econstructon, the Latarget Procedure

• Posterior Labral epairs

• SL P epairs

• iceps endon Patholog , enotom and enodecis

• Subscapularis epairs

• Subacromial ecompression, cromioplast , um ord s

• Partal ears rtcular Sur ace, ursal Sur ace

• Small to edium ears ll nside, ual ow epair

• Large ears ear and ar Sutures

• argin Convergence

• assive ears Partal epairs, iceps utogra , SC , alloon Spacers, endon rans ers

• cromio Clavicular oint econstructons

• Scapula ursoscop

• Pro imal Humeral Head racture i aton

• Hemiarthroplast or ractures

• everse Shoulder rthroplast Some ips and Pearls