With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these a…
In 2005, the hybrid model was published by Prof. H.-D. Alber and Prof. P. Zhu as an alternative to the Allen-Cahn model for the description of phase field transformations. With low interfacial energy, it is more efficient, since the resolution of the diffuse interface is numerically broader for the same solution accuracy and allows coarser meshing. The solutions of both models are associated wi…
The main focus of this thesis is the discussion of stability of an objective (atomic) structure consisting of single atoms which interact via a potential. We define atomistic stability using a second derivative test. More precisely, atomistic stability is equivalent to a vanishing first derivative of the configurational energy (at the corresponding point) and the coerciveness of the second deri…
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space (Ω,Σ,μ)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L1(mT), the space of all functions integrable with respect to the vector measur…
Clustering or cluster analysis [5] is a method in unsupervised learning and one of the most used techniques in statistical data analysis. Clustering has a wide range of applications in many areas like pattern recognition, medical diagnostics, datamining, biology, market research and image analysis among others. A cluster is a set of data points that in some sense are similar to each other, and …
An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling w…
An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical technique…
Proses titik poisson dan proses Markov adalah konsep dasar dalam teori probabilitas dan proses stokastik. Proses titik poisson adalah jenis proses penghitungan yang menggambarkan kejadian acak dari peristiwa dalam waktu atau ruang yang berkelanjutan. Di sisi lain, proses Markov adalah proses stokastik di mana keadaan sistem di masa depan hanya bergantung pada keadaan saat ini, dan bukan pada se…
Bermain-main dengan Resonansi; Sebuah Ajakan untuk Mencari Solusi Periodik Persamaan Diferensial Biasa Orde Dua. Resonansi adalah konsep yang sering muncul di berbagai bidang ilmu dan teknik, termasuk fisika, matematika, teknik, dan musik. Ini mengacu pada fenomena di mana sebuah sistem memiliki frekuensi alami atau getaran yang sesuai dengan frekuensi pemicu eksternal, yang menghasilkan respon…
Epibiota, organisme yang hidup di makhluk hidup lain, adalah sisi menarik dari kehidupan di bumi. Teritip pada paus biru, diatom kecil pada rumput laut besar, lumut hati pada daun palem di bawah pohon di hutan hujan, dan bromeliad tangki besar di mahkota luar pohon raksasa memiliki beberapa kesamaan, tetapi ada juga banyak perbedaan. Rencana awal saya adalah menulis sebuah buku dengan cakupan t…