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"The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Pad approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others)."

"Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures. Scientific Computation on Mathematical Problems and Conjectures includes studies of the Bernstein Conjecture of 1913 in polynomial approximation theory, the "1/9" Conjecture of 1977 in rational approximation theory, the famous Riemann Hypothesis of 1859, and the Polya Conjecture of 1927. The emphasis of this monograph rests strongly on the interplay between hard analysis and high-precision calculations."

"Matrix functions are of growing interest due to their fascinating theory and the many applications in which they provide insight and succinct solutions. Functions of Matrices: Theory and Computation gives a thorough treatment of the theory of matrix functions and numerical methods for computing them, as well as an overview of applications."

"Misalkan terdapat graf G, H dan F. Notasi F -> (G,H) mempunyai arti bahwa setiap pewarnaan merah-biru pada semua sisi graf F mengakibatkan adanya subgraf G berwarna merah atau subgraf H berwarna biru. Pewarnaan-(G,H) pada graf F adalah pewarnaan merah-biru pada semua sisi graf F sehingga tidak ada subgraf G merah maupun subgraf H biru. Graf F adalah graf Ramsey (G,H)-minimal jika F -> (G,H) dan untuk setiap e anggota sisi-sisi pada graf F berlaku (F-e) memiliki pewarnaan-(G,H). Himpunan semua graf Ramsey (G,H)-minimal dinotasikan dengan R(G,H). Himpunan R(G,H) dikatakan berhingga jika banyaknya anggota di R(G,H) berhingga. Bila tidak demikian, dikatakan R(G,H) tak-berhingga.Graf padanan mK2 adalah graf yang terdiri dari m sisi saling lepas. Graf lintasan Pn adalah graf yang terdiri dari satu lintasan dengan n titik. Penelitian pada tesis ini yaitu himpunan Ramsey R(G,H) berhingga. Penelitian berfokus ketika G merupakan graf padanan mK2 dan H merupakan graf lintasan P4 atau P5. Diperoleh semua graf tak-terhubung di R(3K2,P4) dan dua puluh graf terhubung yang bukan graf lingkaran di R(3K2,P4)Selanjutnya, dibahas salah satu operasi yang akan digunakan pada graf Ramsey minimal, yaitu operasi subdivisi. Dibuktikan bahwa jika F ∈ R(2K2,P5) maka setiap graf yang diperoleh dengan subdivisi (5 titik) pada sisi yang bukan pendan di F merupakan graf Ramsey (3K2,P5)-minimal. Kemudian, dilakukan perumuman untuk mengkonstruksi graf Ramsey minimal di R((m+1)K2,Pn) dari graf Ramsey minimal di R(mK2,Pn) untuk m>=4 dan n=4 atau n=5.

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Let F, G, dan H be simple graphs. The notation F -> (G,H) means that any red-blue coloring of all edges of F will contain either a red copy of G or a blue copy of H. (G,H)-coloring on F means a red-blue coloring of all edges of F such that the red copy of G and the blue copy of H cannot be found. A graph F is Ramsey (G,H)-minimal if F -> (G,H) and for each edge element of all edges of F, (F-e) has (G,H)-coloring. The set of all Ramsey (G,H)-minimal graphs will be denoted by R(G,H). The pair (G,H) is called Ramsey-finite if R(G,H) is finite and Ramsey-infinite otherwise.

The matching graph mK2 is a graph consist of m independent edges. The path graph Pn is a graph consist of one path on n vertices. This thesis is about Ramsey finite. The focus is for G is matching graph and H is a path graph P4 or P5. We obtained all disconnected graphs and twenty connected graphs belonging to Ramsey (3K2,P4)-minimal graph.

Moreover, we discuss an operation on Ramsey minimal graphs, namely subdivision operation. We prove that if F ∈ R(2K2,P5) then a graph obtained by subdividing one non-pendant edge (5 times) is a Ramsey (3K2,P5)-minimal graph. Furthermore, we do generalization for constructing Ramsey minimal graphs in R((m+1)K2,Pn) from R(mK2,Pn) for m>=4 and n=4 or 5"

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Menurut Badan Pusat Statistik Indonesia (BPS) dalam sepuluh tahun terakhir (2007-2017) jumlah perusahaan konstruksi relatif meningkat setiap tahun rata-rata 7,82%, kondisi ini mengakibatkan peningkatan daya saing konstruksi perusahaan dalam memenangkan lelang. Kegiatan estimasi yang tepat diharapkan dalam proses lelang untuk memenangkan lelang pada harga yang kompetitif. Sulit bagi kontraktor untuk menentukan harga penawaran karena adanya risiko yang mempengaruhi penentuan harga proyek. Karena itu, strategi penawaran perlu dikembangkan dengan mengidentifikasi hal yang perlu dipertimbangkan dari tahap lelang berbasis risiko. Dalam studi ini, kami mengidentifikasi kegiatan dan output dari setiap proses pada tahap lelang yang perlu dipertimbangkan dalam proses estimasi  dan menganalisis risiko yang mungkin timbul dalam setiap proses tender. Data diperoleh melalui studi literatur dan kuesioner, kemudian diolah dengan analisa regresi dan analisa risiko. Hasil dari penelitian ini tahapan menerima informasi tender, keputusan keikutsertaan tender, penentuan tim tender, mengambil dan mempelajari dokumen lelang, mengikuti penjelasan lelang, peninjauan lapangan, penentuan jadwal pelaksanaan, penentuan metode kerja, kebutuhan jaminan penawaran, perhitungan harga penawaran hingga kelengkapan dokumen administrasi dan teknis berpengaruh terhadap kinerja lelang. Dengan 5 variabel berisiko tinggi yaitu data BQ tidak lengkap, kemungkinan kontraktor atau penyedia jasa akan mengalami kerugian, perhitungan volume tidak akurat, dan kurangnya informasi mengenai tender yang akan datang.

 

Kata kunci: Strategi Penawaran; Penawaran yang kompetitif; Kinerja lelang; Proses estimasi

 

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According to the Indonesian Central Bureau of Statistics (BPS) in the last ten years (2007-2017) the number of construction companies has increased by an average of 7.82% every year, this condition has resulted in an increase in the company`s construction competitiveness in winning the auction. Appropriate estimation activities are expected in the auction process to win the auction at competitive prices. It is difficult for contractors to determine the bid price because of the risks that affect project pricing. Therefore, the bidding strategy needs to be developed by identifying things to consider from the risk-based auction stage. In this study, we identify the activities and outputs of each process at the auction stage that need to be considered in the estimation process and analyze the risks that may arise in each tender process. Data obtained through literature study and questionnaire, then processed with regression and risk analysis. The results of this study are stages of receiving tender information, tender participation decisions, determination of tender teams, taking and studying auction documents, following auction explanations, field review, determination of implementation schedule, work method determination, bid guarantee requirements, bid price calculation to administrative documents and technical effect on auction performance. With 5 high risk variables, namely BQ data is incomplete, it is likely that the contractor or service provider will experience losses, inaccurate volume calculations, and lack of information regarding upcoming tenders.

 

Keywords: Bidding Strategy; Competitive Bidding; Auction Performance; Estimation Process

 

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