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Abstrak :
Asuransi kendaraan bermotor diperlukan untuk mengantisipasi berbagai risiko kerugian yang mungkin timbul dari kepemilikan dan/ atau penggunaan kendaraan. Umumnya dalam perhitungan premi asuransi kendaraan, digunakan faktor – faktor yang teramati dari tertanggung, contohnya domisili, jenis kelamin, dan usia tertanggung. Akan tetapi, faktor – faktor tidak teramati, seperti kemampuan dan perilaku berkendara dari tertanggung berpengaruh penting dalam frekuensi klaim yang dihasilkan. Sehingga, digunakan riwayat klaim tertanggung yang diekspektasikan menampung pengaruh dari faktor tidak teramati. Sistem penentuan besar premi yang turut melibatkan faktor tertanggung yang tidak teramati disebut sebagai sistem Bonus Malus. Bonus merupakan penurunan premi apabila seorang tertanggung tidak mengajukan klaim sama sekali dalam satu periode dan Malus merupakan kenaikan premi apabila seorang tertanggung mengajukan satu atau lebih klaim. Pada tugas akhir ini, dilakukan perhitungan relativitas optimal atau koefisien penyesuaian premi pada sistem Bonus Malus -1/Top Scale dan -1/+2. Sistem -1/Top Scale memberlakukan penurunan sebanyak satu level jika tidak ada klaim yang dilaporkan dan perpindahan tertanggung ke level tertinggi jika ada klaim, sedangkan sistem -1/+2 menerapkan perpindahan sebanyak dua level ke atas jika terdapat klaim dan penurunan satu level ke bawah jika tidak ada klaim yang dilaporkan. Simulasi perhitungan diterapkan pada sebuah portofolio data asuransi kendaraan negara Perancis yang melibatkan 328760 polis. Diperoleh bahwa selisih relativitas optimal atau koefisien penyesuaian premi untuk setiap level pada sistem -1/+2 tidak sebesar sistem -1/+Top Scale. ......Automobile insurance is required to protect policyholders from financial loss caused by car damage, accidents, or theft. In general, observable characteristics such as residence, gender, and the insured's age are considered in the process of determining motor insurance premiums. However, several unobservable characteristics, like as driver competence and behavior, have a significant impact on claim frequency. As a result, the insured's claim history is used and expected to account for the impact of unobservable circumstances. The Bonus Malus methodology is a method of assessing the amount of the premium that also includes the insured factors that are not able to be observed. Bonus is a decrease in premium if the insured generates no claims in a particular period of time, whereas a Malus is an increase in premium if the insured has one or more claims. The final project focuses on the determination of appropriate relativity or premium adjustment coefficients for the Bonus Malus -1/Top Scale dan -1/+2 systems. -1/Top Scale system applies a one-level drop if no claims are reported and a switch to the highest level if there is one or more claims reported, while the -1/+2 system applies a two-levels increase if there is a claim and a decrease a one-level decrease if no claims are reported. The simulation is applied to a French national auto insurance data portfolio involving 328760 policies. It is discovered that the difference in the optimal relativity or premium adjustment coefficient for each level in the -1/+2 system is not as large as the -1/Top Scale system.

Abstrak :
Acquaints the specialist in relativity theory with some global techniques for the treatment of space-times and will provide the pure mathematician with a way into the subject of general relativity.

Abstrak :
Mathematical modeling he ability to apply mathematical concepts and techniques to real-life systems as expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.

Abstrak :
Predictive theories of phenomena involving phase change with applications in engineering are investigated in this volume, e.g. solid-liquid phase change, volume and surface damage, and phase change involving temperature discontinuities. Many other phase change phenomena such as solid-solid phase change in shape memory alloys and vapor-liquid phase change are also explored. Modeling is based on continuum thermo-mechanics. This involves a renewed principle of virtual power introducing the power of the microscopic motions responsible for phase change. This improvement yields a new equation of motion related to microscopic motions, beyond the classical equation of motion for macroscopic motions. The new theory sensibly improves the phase change modeling. For example, when warm rain falls on frozen soil, the dangerous black ice phenomenon can be comprehensively predicted. In addition, novel equations predict the evolution of clouds, which are themselves a mixture of air, liquid water and vapor.

Abstrak :
The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

Abstrak :
This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects.