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Abstrak :
Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem. The algorithms and software at the "leaves" of the decision tree range from the classical QR algorithm, which is most suitable for small dense matrices, to iterative algorithms for very large generalized eigenvalue problems. Algorithms are presented in a unified style as templates, with different levels of detail suitable for readers ranging from beginning students to experts. The authors' comprehensive treatment includes a treasure of further bibliographic information.

Abstrak :
This clearly written, self-contained volume studies the basic equations of kinetic theory in all of space. It contains up-to-date, state-of-the-art treatments of initial-value problems for the major kinetic equations, including the Boltzmann equation (from rarefied gas dynamics) and the Vlasov-Poisson/Vlasov-Maxwell systems (from plasma physics). This is the only existing book to treat Boltzmann-type problems and Vlasov-type problems together. Although these equations describe very different phenomena, they share the same streaming term. The author proves that solutions starting from a given configuration at an initial time exist for all future times by imposing appropriate hypotheses on the initial values in several important cases. He emphasizes those questions that a mathematician would ask first: Is there a solution to this problem? Is it unique? Can it be numerically approximated? The topics treated include the study of the Boltzmann collision operator, the study of the initial-value problem for the Boltzmann equation with "small" and "near equilibrium" data, global smooth solvability of the initial-value problem for the Vlasov-Poisson system with smooth initial data of unrestricted size, conditions under which the initial-value problem for the Vlasov-Maxwell system has global-in-time solutions (in both the smooth and weak senses), and more.

Abstrak :
In this paper, we give another proof about the relationship between AB and BA with eigenvalue zero that reduced by structure Jordan for nilpotent matrix

Abstrak :
In this paper, we give another proof about the relationship AB and BA with eigenvalue zero that reduced by structure Jordan for nilpoten matrix

Abstrak :
Slow back-loaded pattern highlights challenges and raises a specific concern over the quality of state budget (APBN) implementation in West Sumatera Province. This study aims to investigate factors constraining state budget (APBN) absorption in 2017 which directly causes the existence of such a pattern. A set of questionnaires were used to collect primary data. Exploratory Factor Analysis (EFA) was utilized to identify latent variables underlying the scale and SPSS.22 was employed to test questionnaires from 200 working units that involved in this research. The findings explain that six main factors influencing state budget absorption in West Sumatera were a. Goods and Services Procurement, b. Internal Policy Changes, c. Budget Planning, d. Financial Officers, e.Changes on Government Policy and f. Document Verification Process on Budget Execution. This study recommends that working units should prepare for early procurement to expedite the budget absorption.

Abstrak :
ABSTRAK
Dalam analisis multivariate klasik dalam suatu uji hipotesa sering digunakan analisis nilai eigen dalam penetuan statistik ujinya. Dibawah kondisi H0, nilai statistik uji yang diperoleh akan digunakan untuk bentuk distribusi yang berkaitan dengan statistik uji. Daerah kritis penolakan suatu uji uji hipotesa ditentukan berdasarkan bentuk distribusi yang diperoleh. Nilai eigen yang diperoleh untuk analisi multivariat ini untuk pembentukan statistik ujinya bisa menggunakan fungsi yang melibatkan keseluruhan nilai eigen atau dengan menggunakan nilai yang ekstrem. Untuk nilai eigen yang maksimum statistik uji yang digunakan berdasar Roy test maksimum. Cara lain yang digunakan adalah dengan pendekatan distribusi Tracy-Widom. Disamping daerah kritis yang diperoleh juga dibutuhkan p-value berdasar nilai statistik uji yang sebenarnya.

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ABSTRACT
Clasical multivariate analysis in test hipothesa H0 most used eigen analysis in determined their test statistics . Under H0 test statistics which founded wiil be used to make distribution concerning with test statistics. Critical area H0 determined their distributions. Eigenvalue which founded will be used to build test statistics may included entilrely or eigen value maximum. Roy maximum test had used maximum eigen value for inference by Tracy-Widom distribution. Besides founded critical area, for also wanted p-value for their test statistics which had found

Abstrak :
Graf prisma adalah graf yang bersesuaiandengan kerangkabangun ruangprisma. Hanya graf prismaberarahsiklik dengan pola tertentu yang diperhatikandalam penelitian ini. Graf prismaberarahsiklik dinotasikan 𝑌𝑚(𝑚≥3),di mana 𝑚adalah setengah jumlah simpul,dan memiliki 2𝑚 simpul dan3𝑚busur. Sebuah graf dapat direpresentasikanmenggunakansebuah matriks. Ada beberapa jenis matriks yang biasanya digunakan dalam merepresentasikan graf. Diantaranya adalah matriks adjacency, anti-adjacency, dan Laplacianyang dibahas dalam penelitian ini. Polinomial karakteristik dari matriks adjacency, matriks anti-adjacency, dan matriks Laplaciandari graf prisma berarah siklik 𝑌𝑚diperoleh beserta nilai-nilaieigen real dan kompleksnya. Metode yang digunakan untuk membuktikan hasil-hasil penelitian iniadalah operasi baris matriks dan faktorisasi. Adapununtukpolinomial karakteristik dari matriks anti-adjacency𝑌𝑚, hasilnya dibuktikan dengan mengamati subgraf terinduksi siklik dan asiklik dari 𝑌𝑚berdasarkan sebuah teorema yang ditemukan dalam penelitian sebelumnya.

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A prism graph is a graph which corresponds to the skeleton of a prism. Only directed cyclic prism graphs with certain pattern are considered in this research. The directed cyclic prism graph is denoted 𝑌𝑚(m≥3),where 𝑚is half the number of vertices,and has 2𝑚vertices and 3𝑚edges.Agraph can be represented by usinga matrix. There are several types of matrices that are usually used in representing a graph. Among them aretheadjacency, anti-adjacency, and Laplacianmatriceswhich are discussedinthis research. The characteristic polynomialsof theadjacency matrix,theanti-adjacency matrix, and the Laplacian matrix of directed cyclic prism graph 𝑌𝑚are obtainedas well as their real and complex eigenvalues. The methods used toprovethe results are matrix row operations and factorizations.As for the characteristic polynomial of the anti-adjacency matrix of 𝑌𝑚, the results are proved byobserving the both cyclic and acyclic induced subgraphs of 𝑌𝑚according to a theorem invented in a previous research