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"Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed."

"This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity."

"Aljabar Lie adalah ruang vektor atas suatu lapangan yang dilengkapi dengan bracket Lie yang bilinier, bersifat antisimetri dan memenuhi identitas Jacobi. Salah satu contoh dari aljabar Lie adalah himpunan pemetaan linier dari ruang vektor V ke V, yang dinotasikan dengan gl(V), dengan bracket Lie berupa komutator. Jika V adalah suatu aljabar, maka himpunan derivasi dari V (dinotasikan dengan Der(V)) membentuk suatu subaljabar Lie dari gl(V). Holomorph dari aljabar Lie L, yaitu hasil tambah langsung dari L dan Der(L), juga membentuk aljabar Lie. Aljabar Lie dikatakan lengkap jika pusatnya adalah himpunan nol dan semua derivasinya adalah derivasi dalam. Pada tesis ini, diulas syarat yang harus dipenuhi agar aljabar derivasi dan holomorph dari suatu aljabar Lie menjadi lengkap.

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Lie algebra is a vector space over a field together with a bilinear Lie bracket, that satisfy antisymmetry and Jacobi identity. One of the examples of Lie algebra is a set of linear transformation from a vector space V to V, that is denoted by gl(V), with a commutator as the Lie bracket. If V is an algebra then the set of derivation of V (denoted by Der(V)) forms a Lie subalgebra of gl(V). The holomorph of a Lie algebra, that is direct sum of vector spaces L and Der(L), also forms a Lie algebra. A Lie algebra is called complete if its center is zero and all its derivations are inner. In this thesis, it is discussed the properties that must be satisfied in order to the derivation and the holomorph of Lie algebra become complete."

"The emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Volume 2 builds on the fundamentals presented in Volume 1, delving deeper into relationships among stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry."

"Aljabar Lie sederhana merupakan aljabar Lie dengan karakteristik khusus, yaitu tidak abelian dan tidak memiliki ideal sejati yang tak nol. Dalam penelitian ini, dikenalkan suatu aljabar Lie sederhana yaitu sl fr infin;,K yang merupakan subaljabar Lie dari gl fr infin;,K . Aljabar Lie sederhana sl fr infin;,K memiliki dimensi yang tidak berhingga dengan basis yang tak terhitung.

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Simple Lie algebra is Lie algebra with special characteristics, which is not abelian and not having any nonzero proper ideal. In this study, a simple Lie algebra sl fr infin ,K is introduced, which is a sub Lie algebra from gl fr infin ,K . Simple Lie algebra sl fr infin ,K has an infinitely dimension with an uncountably basis."

"Banyak sekali tindak kejahatan yang sulit untuk diungkap oleh aparat penegak hukum karena sulit menemukan bukti-bukti serta informasi yang minim di lapangan karena pelaku tindak kejahatan selalu berusaha semaksimal mungkin untuk tidak meninggalkan jejak agar kasusnya tidak dapat terungkap sehingga penyidik membutuhkan instrumentasi untuk mendukung mengungkap tindak kejahatan. Instrumentasi tersebut salah satunya adalah dengan menggunakan alat Lie Detector. Alat lie detector didesain untuk melihat perilaku tubuh manusia saat dalam kondisi tertekan. Alat ini tidak dapat secara spesifik mendeteksi apakah seseorang berbohong atau tidak. Lie detector hanya mengukur reaksi psikologis manusia sebagai indikasi seseorang berbohong atau tidak. Seorang pembohong ?kelas kakap? mungkin biasa bersikap sangat tenang sehingga reaksi psikologisnya tak terdeteksi. Dalam hal ini operator lie detector mesti benar-benar berpengalaman. Di negara maju, khususnya Eropa dan Amerika Serikat, lie detector sudah sering digunakan dan menjadi prosedur standart dalam memeriksa penjahat dan dalam mengungkapkan kasus kriminal. dengan kata lain, penjahat bila ingin perkaranya sampai di pengadilan, dia harus melalui test dengan alat ini dahulu. Pelaksanaannya dilakukan pihak independen (independent examiner), biasanya seorang psikolog, dan hasil akhir untuk menilai tingkat kebohongan itu juga di tangan psikolog. Polisi yang menangani kasus akan menerima hasil yang sudah matang dari psikolog tersebut. Ahli hukum di sana berpendapat, psikolog tentunya akan lebih memahami masalah kejiwaan, sehingga apabila pemeriksaan lie detector dilakukan oleh psikolog, maka hasilnya akan lebih akurat dan obyektif. Alat ini dikenal dengan nama Polygraph Test.

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There are so many crime that are difficult to be revealed by law enforcement officials it because less of information and evidence that made by the criminals. Criminals always try not to make any trace of evidence so that the case can not be revealed, the investigator need an instrumentation to support revealing the crimes. One of the instrument is using the lie detector. Lie detector was designed to view the conduct of human body in the pressured condition. Lie detector can not specifically detect whether a person is lying or not. Lie detector only measuring a human reaction as an indication of a person's psychological. An expert liar usually can act very quiet so that the phsycological reaction is hard to be detected. In this case the examiner of lie detector must have an experienced. In the advance country, especially in Europe and USA, lie detector is often to used and already become standart procedure to examining the criminals and to revealing the criminal cases. The implementation do by the independent examiner, usually a psychologist and the assessment result also in the hands of psychologists. The police who handled the case will receive the results from the psychologist. The legal experts in there argued that the psychologists would be more understand of the psychological problems. so that if the lie detector examination do by a psychologist, then the result would be more accurate and objective. The lie detector examination is known as the Polygraph Test."

"Penggunaan hasil pemeriksaan poligraf yang dijadikan alat bukti dalam praktik peradilan pidana Indonesia seharusnya dapat diiringi dengan keberadaan regulasi yang memadai serta mekanisme pengawasan yang jelas terhadap pelaksanaan pemeriksaan poligraf agar dapat sejalan dengan asas due process of law. Hal tersebut tentunya berkaitan pada keabsahan suatu alat bukti yang dihadirkan dalam persidangan di pengadilan, mengingat keabsahan suatu alat bukti dapat ditentukan dengan melihat ke belakang terkait kesesuaian tata cara perolehan alat bukti tersebut dengan ketentuan hukum yang berlaku. Penelitian ini dilakukan dengan menggunakan metode penelitian kualitatif dengan bentuk penelitian yuridis normatif. Skripsi ini akan membahas mengenai pemeriksaan poligraf dalam praktik peradilan pidana Indonesia mulai dari regulasi yang berlaku saat ini dan perbandingannya dengan yang berlaku dalam negara Common Law System yaitu Negara Bagian New Mexico di Amerika Serikat, serta peran dan keabsahan alat bukti yang bersumber dari hasil pemeriksaan poligraf dalam praktik peradilan pidana di Indonesia, yang kemudian akan dianalisis keterkaitannya dengan asas due process of law. Kesimpulan dari penelitian ini adalah pemeriksaan poligraf dan penggunaannya di Indonesia saat ini belum diatur secara lengkap, serta tidak terdapat mekanisme pemeriksaan keabsahan dari perolehan alat bukti yang bersumber dari hasil pemeriksaan poligraf, dan penggunaan instrumen pemeriksaan poligraf telah bertentangan dengan asas due process of law. Oleh karena itu, perlu adanya pembahasan lebih lanjut untuk mengkaji penggunaan instrumen pemeriksaan poligraf sebagai alat bukti.

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The usage of polygraph examination results that are used as evidence in Indonesian criminal justice practices should be accompanied by the existence of adequate regulations and obvious supervisory mechanisms for the enforcement of polygraph examination, so it could be in line with the due process of law principle. This is certainly related to the validity of the evidence presented in a trial at the court, considering the validity of evidence can be determined by observing the conformity of the procedure for obtaining the evidence with the provisions of applicable law. This research is conducted using qualitative research methods with normative juridical forms of research. This thesis will discuss the polygraph examination in Indonesian criminal justice practices starting from the current applicable regulation and its comparison with those applicable in the Common Law System, namely in the State of New Mexico in the United States of America, as well as the role and validity of the evidence that derived from the result of a polygraph examination in Indonesian criminal justice practices, which will be analyzed about the correlation with the due process of law principle. The conclusion of this thesis are the polygraph examination and its current application in Indonesia are not fully regulated, furthermore there is no supervisory mechanism for checking the validity of the acquisition of evidence derived from the results of the polygraph examination, thus it is not proven to fulfill the due process of law principle. Therefore, there needs to be a further discussion to examine the use of the polygraph examination instruments as evidence."

"This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity."