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"This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platonic solids, Euler’s formula, irrational numbers, countable sets, permutations, and a proof of the pythagorean theorem. All of these topics serve a single compelling goal, understanding the mathematical patterns underlying the symmetry that we observe in the physical world around us."

"Mathematical symmetry and chaos come together to form striking, beautiful color images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns.The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter."

"ABSTRAKLatar Belakang: Asimetri pada wajah dan lengkung gigi merupakan fenomena yang dapat ditemui hampir pada seluruh individu sehingga saat ini asimetri dengan batas-batas tertentu masih dianggap seimbang secara klinis dan dinilai normal. Asimetri mandibula merupakan asimetri yang paling sering terjadi dan mudah terlihat dikarenakan mandibula adalah bagian wajah yang paling mudah bergerak dibandingkan bagian wajah lainnya. Asimetri mandibula ditemukan paling tinggi dan dapat memengaruhi perawatan. Untuk mendiagnosis asimetri mandibula dapat dilakukan dengan pemeriksaan klinis ekstra oral yang meliputi pemeriksaan smile symmetry. Tujuan: Mengetahui frekuensi dan distribusi terjadinya asimetri mandibula pada mahasiswa angkatan tahun 2016 FKG UI dan mengetahui berapa persen mahasiswa yang mengalami asimetri mandibula. Metode: Metode yang digunakan pada penelitian ini adalah analisis gambaran klinis yang dilakukan untuk melihat adanya asimetri atau disporposi pada wajah tampak frontal khususnya pada mandibula. Analisis dilakukan dengan cara fotografi frontal dalam kondisi standar dan kondisi gigi tersenyum. Kesimpulan: Pada mahasiswa FKG UI angkatan 2016 terdapat 37 subjek (32,2%) dengan asimteri mandibula dan terdapat 57 subjek (49,6%) yang memiliki senyum tidak simetris.

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ABSTRACT

Background: Facial asymmetry is a phenomenon found in almost every individual, thus asymmetry within certain boundaries is accepted as clinically balanced and normal. Mandibular asymmetry is the most common asymmetry that can occur and is easily seen because the mandibula is the part of the face that is most mobile compared to the rest of the face. Mandibular asymmetry are the most common asymmetry that can affect treatment for asymmetry. Mandibular asymmetry can be diagnosed by extra oral clinical examination which includes smile symmetry. Objective: Knowing the frequency and distribution of mandibular asymmetry in In Faculty Of Dentistry batch 2016 students and knowing what percentage of students experience mandibular asymmetry. Method: The method used in this research is clinical image analysis which is used to see whether asymmetry or facial disproportion on the frontal face image, especially on the mandibula, is present. The analysis is done via frontal photography in a standard setting. Conclusion : In Faculty Of Dentistry batch 2016, there were 42 subjects with mandibular asymmetry and 58 subjects with asymmetry smile."

"A discussion of developments in the field of bifurcation theory, with emphasis on symmetry breaking and its interrelationship with singularity theory. The notions of universal solutions, symmetry breaking, and unfolding of singularities are discussed in detail. The book not only reviews recent mathematical developments but also provides a stimulus for further research in the field."

"This book highlights the symmetry properties of acoustic fields and describes the gauge invariance approach, which can be used to reveal those properties. Symmetry is the key theoretical framework of metamaterials, as has been demonstrated by the successful fabrication of acoustical metamaterials. The book first provides the necessary theoretical background, which includes the covariant derivative, the vector potential, and invariance in coordinate transformation. This is followed by descriptions of global gauge invariance (isotropy), and of local gauge invariance (anisotropy). Sections on time reversal symmetry, reflection invariance, and invariance of finite amplitude waves round out the coverage. "

"Latar Belakang: Deviasi atau ketidakseimbangan proporsi fasial serta hubungan gigigeligi yang menggangu fungsi, estetika dan profil wajah. Bedah ortognatik bertujuan memperbaiki ketidakharmonisan dan estetika wajah bekerjasama dengan perawatan ortodonti. Sagital split osteotomy merupakan reposisi segmen mandibula yang dilakukansecara bilateral. Perubahan posisi kondilus mandibula serta stabilitas skeletal pada pasien BSSO mempengaruhi asimetri kondilus mandibula yang dikaitkan dengan adanya resiko terjadinya TMD.Tujuan: Mengetahui perbedaan kondilus mandibula pada pasien pra bedah dan pasca bedah BSSO di Divisi Bedah Mulut dan Maksilofasial RSCM, Jakarta dengan perhitungan indeks simetri dan asimetri kondilus mandibula. Material dan Metode: Penelitian retrospektif melalui radiografik panoramik pra bedah, pasca bedah dan 1 tahun pasca bedah BSSO prosedur setback mandibula di Divisi Bedah Mulut danMaksillofasial, RSCM, Januari 2001 hingga Desember 2017 sesuai kriteria inklusi dan eksklusi dan didapatkan 16 sampel. Setiap sampel dilakukan pengukuran pada radiografi panoramiknya dengan menggunakan teknik Habets dan teknik Kjellberg.Hasil Penelitian: Haasil uji Repeated ANOVA, didapatkan hasil kemaknaan p = 0.389 maka p>0.05 pada indeks asimetri Habets pada saat pra bedah, pasca bedah dan 1 tahun pasca bedah,. Sedangkan uji Repeated ANOVA kelompok indeks simetri Kjellberg, didapatkan hasil kemaknaan p = 0.297 maka p>0.05 pada indeks asimetri Kjellberg pada saat pra bedah, pasca bedah dan 1 tahun pasca bedah.Kesimpulan: Hasil penelitian indeks asimetri Habets dan indeks simetri Kjellberg menunjukkan tidak ada perbedaan signifikan pada hasil pengukuran simetri dan asimetri mandibula. Orientasi kodilus terhadap fossa glenoid dan manuver posisi kondilus merupakan langkah terpenting yang harus dilakukan dalam BSSO.sehingga tujuan pokokBSSO yaitu perbaikan fungsi, estetik dan stabilitas dapat tercapai.

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Background: Deviations or imbalances in facial proportions and occlusions that interfere with facial function, aesthetics and profile. Orthognathic surgery aims to correct the disharmony and facial aesthetics in collaboration with orthodontic treatment. Sagittal split

osteotomy is repositioning of the bilateral mandible segment. Changes in mandibular condyle position and bone stability in BSSO affect mandibular condyle asymmetry related to TMD risk.

Objective: To determine the differences in mandibular condyle in pre-surgical and postBSSO patients in the Oral and Maxillofacial Surgery Division, RSCM, by calculating the symmetry index and asymmetry of the mandibular condyle.

Materials and Methods: Retrospective studies through preoperative, postoperative and 1 year post-BSSO mandibular setback procedures panoramic radiographs in the Oral and Maxillofacial Surgery Division, RSCM, January 2001 to December 2017 according to inclusion and exclusion criteria and obtained 16 samples. Each sample was measured on its panoramic radiography using the Habets technique and the Kjellberg technique.

Result: The results of repeated ANOVA test obtained significance p = 0.389 then p> 0.05 in the Habet asymmetry index during pre-surgery, post-surgery and 1 year post-surgery. Whereas the Repeated ANOVA test from the Kjellberg symmetry index group, the result of significance was p = 0.297, then p> 0.05 on the Kjellberg asymmetry index during presurgery, post-surgery and 1 year post-surgery.

Conclusion: The results of the Habets asymmetry index and the Kjellberg symmetry index showed no significant differences in the results of measurements of mandibular symmetry and asymmetry. Condyle orientation to the glenoid fossa and condyle position maneuver are the most important steps that must be done in BSSO. So that the main objectives of BSSO are improvement of function, aesthetics and stability can be achieved."

"[ABSTRAKTesis ini bertujuan untuk menganalisis hubungan antara kebiasaan mengunyah dan asimetri vertikal kondilus pada pasien TMD. Dilakukan penelitian potong lintang di klinik Prostodonsia RSKGM FKG UI menggunakan data sekunder dari empat puluh rekam medik dan gambaran radiografik pasien TMD. Tracing gambaran radiografi panoramik dilakukan untuk menilai asimetri vertikal kondilus pada subjek menggunakan Indeks Asimetri Habets dan Simetri Indeks Kjellberg.Hasil penilaian asimetri vertikal kondilus kemudian dihubungkan dengan kebiasaan mengunyah, Indeks Helkimo, dan DC/TMD. Hasil penelitian menunjukkan tidak terdapat hubungan antara kebiasaan mengunyah dan asimetri vertikal kondilus pada pasien TMD.

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ABSTRACTThis study was performed to analize the relationship betweenchewing preferences and condylar asymmetry in patients with TMD. A cross-sectional study at Prosthodontic Clinic, Faculty of Dentistry, University of Indonesia using secondary data obtain from forty TMD patients's medical record and panoramic radiograph was conducted. The panoramic radiograph were traced on tracing paper to evaluate condylar asymmetry using Asymmetry Index of Habets and Symmetry Index of Kjellberg. The evaluation of condylar asymetry were then related to chewing preference, Helkimo?s Index, and DC/TMD.There was no relationship found between chewing preference and condylar asymmetry in patients with TMD. , This study was performed to analize the relationship betweenchewing preferences and condylar asymmetry in patients with TMD. A cross-sectional study at Prosthodontic Clinic, Faculty of Dentistry, University of Indonesia using secondary data obtain from forty TMD patients’s medical record and panoramic radiograph was conducted. The panoramic radiograph were traced on tracing paper to evaluate condylar asymmetry using Asymmetry Index of Habets and Symmetry Index of Kjellberg. The evaluation of condylar asymetry were then related to chewing preference, Helkimo’s Index, and DC/TMD.There was no relationship found between chewing preference and condylar asymmetry in patients with TMD. ]"

"Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures."

"Latar Belakang: Keseimbangan dan harmoni gambaran wajah merupakan tujuan utama dari penatalaksanaan bedah pada pasien dengan celah bibir. Berbagai metode operasi untuk celah bibir unilateral telah tersedia. Labioplasti metode Cronin pada pasien celah bibir dan langit-langit unilateral menghasilkan bibir yang simetris dengan jaringan parut seminimal mungkin.Tujuan: Evaluasi kesimetrisan bibir pada pasien celah bibir dan langit-langit unilateral pasca labioplasti metode Cronin sesuai protap yang berlaku di Unit Celah Bibir dan Langit-langit Rumah Sakit Anak dan Bunda Harapan Kita Jakarta.Metode: Pasien celah bibir dan langit-langit unilateral 2 minggu, 1 bulan, 3 bulan, 6 bulan, dan 1 tahun pasca labioplasti dengan metode Cronin sebanyak 36 orang dinilai kesimetrisan bibir secara antropometri dengan fotograf yang telah terstandarisasi dari 2 aspek, yaitu anterior dan lateral. Bibir pada sisi celah diukur dan dibandingkan dengan sisi non celah.Hasil: Tidak terdapat perbedaan bermakna pada jarak ac ke komisura ipsilateral (p = 0.387) dan jarak puncak cupid?s bow ke komisura ipsilateral (p = 0.933) pada sisi celah dan non celah. Terdapat perbedaan bermakna jarak sbal ke puncak cupid?s bow (p = 0.007) antara sisi celah dan non celah pada 2 minggu, 1 bulan, 3 bulan, dan 6 bulan pasca labioplasti.Kesimpulan: Kesimetrisan bibir pada sisi celah dan non celah pasca labioplasti dengan metode Cronin berdasarkan rasio pengukuran antropometri dengan fotograf yang telah terstandarisasi dapat dicapai sempurna pada 1 tahun pasca labioplasti.

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Background: Balance and harmony of facial features are the goal of surgical treatment for patients with cleft lip. Various methods of surgery for unilateral cleft lip had been provided. Labioplasty Cronin method in patients with unilateral cleft lip and palate produce symmetrical lips with minimal scarring.

Objective: Evaluation lip symmetry post labioplasty Cronin method in patients with unilateral cleft lip and palate based on standard operating procedure in Cleft Center Harapan Kita General Hospital.

Material and Methods: Thirty-six patients with unilateral cleft lip and palate after performing labioplasty Cronin method were photographed on anterior and lateral side by a standardized method 2 weeks, 1 month, 3 months, 6 months, and 1 year after surgery. Lips on the cleft side were measured and compared with the opposite side.

Results: There were no significant differences the length of ac to ipsilateral commissure (p = 0.387) and the distance of the peak cupid's bow to the ipsilateral commissure (p = 0.933) on cleft and norm side. There are significant differences the length of sbal to the Cupid's bow peak (p = 0.007) between cleft and norm side at 2 weeks, 1 month, 3 months, and 6 months post labioplasty.

Conclusion: Symmetrical lip post labioplasty with Cronin method at cleft and non cleft side based on the ratio of anthropometric measurements with standardized photographs can be accomplished perfectly in 1 year after labioplasty."