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"Misalkan T adalah gelanggang matriks segitiga formal dan T[z; θ, d] adalah gelanggang polinomial miring atas T. Dengan mempelajari homomorfisma khusus dan derivasi miring pada gelanggang matriks segitiga formal, dapat dibuktikanbahwa gelanggang polinomial miring T[z; θ, d] memiliki representasi matriks segitiga formal.

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Let T be a formal triangular matrix ring and T[z; θ, d] be a skew polynomial ring over T. By studying a particular ring homomorphism and skew derivation on formal triangular matrix ring, one can show that the skew polynomial ring T[z; θ, d] has formal triangular matrix representation."

"Graf merupakan himpunan simpul dan busur dengan setiap busurnya menghubungkan dua simpul. Graf dapat direpresentasikan dalam sebuah matriks. Matriks representasi graf di antaranya yaitu matriks ketetanggaan, matriks jarak, matrik kehadiran, dan matriks Laplacian. Matriks ketetanggaan merepresentasikan ada tidaknya busur yang menghubungkan dua buah simpul. Matriks jarak merepresentasikan jarak lintasan terpendek antara dua simpul pada graf. Pada graf berdiameter dua, yaitu jarak terpanjang di antara dua simpul adalah dua. Graf berdiameter dua di antaranya yaitu graf bipartit, graf roda, dan graf kipas. Pada tesis ini akan dibahas hubungan antara matriks ketetanggaan dan matriks jarak dari suatu graf berdiameter dua, dan sifat-sifat matriks jarak pada graf berdiameter dua, serta polinomial karakteristik dari matriks jarak pada kelas graf khusus berdiameter dua yaitu graf bipartit lengkap 𝐾𝑛,𝑛.

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Graph is the set of vertices and edges where each edge connects two vertices. The graph can be represented by a matrix. There are several matrix representation of graph, such as adjacency matrix, distance matrix, incidence matrix, and Laplacian matrix. The adjacency matrix represents the presence or absence of an arc connecting two vertices. Distance matrix represent the shortest path between two vertices on a graph. The example of two-diameter graphs are bipartite graphs, wheel graphs, and fan graphs. In this thesis we discuss the relationship between the adjacency matrix and the distance matrix of a two-diameter graph, and the properties of the distance matrix in the twodiameter graph, and the characteristic polynomial of the distance matrix of special family of two-diameter graph that is complete bipartite graph 𝐾𝑛,𝑛."

"Training merupakan salah satu aspek yang diatur di dalam CPOB yang menjadi hal penting untuk dilakukan dan diberikan oleh industri farmasi kepada setiap personil untuk menyiapkan personil yang terkualifikasi. Adanya keperluan akan dokumentasi terkait daftar training untuk operator produksi yang selama ini belum terdokumentasikan dengan baik di PT. Darya-Varia Laboratoria Plant Gunung Putri, sehingga dilakukannya pengerjaan tugas khusus ini untuk menyusun dan membentuk matriks training plan operator produksi. Metode penyusunan dan pembentukan matriks training plan dilakukan dengan membentuk klasifikasi bagian produksi sesuai penerapannya di PT. Darya Varia Laboratoria Plant Gunung Putri kemudian dilakukan pemilahan dan pengklasifikasian SOP dan batch manufacturing record sebagai dasar pelatian dan langkah terakhir dilakukan pembuatan materi training beserta bahan evaluasi training yang dilengkapi dengan matriks kualifikasi operator sesuai hasil evaluasi training yang dilakukan. Hasil dari penyusunan dan pembentukan matriks training plan untuk bagian general pharmacy didapatkan sebanyak 83 training plan untuk bagian mixing, 73 training plan untuk bagian filling, dan 33 training plan untuk bagian tulle, sedangkan untuk bagian soft capsule didapatka 58 training plan untuk bagian gelatin, 62 training plan untuk bagian mixing dan compounding, 63 training plan untuk bagian enkapsulasi, 49 training plan untuk bagian inspeksi dan drying, 56 training plan untuk bagian sortir dan printing, 52 training plan untuk bagian polishing, dan 59 training plan untuk bagian striping. Bahan evaluasi training yang dihasilkan sebanyak 71 bagian sesuai dengan jumlah SOP bagian produksi dengan masing masing bagian terdiri dari 10 hingga 20 soal dan juga terbentuk kriteria kualifikasi operator berdasarkan nilai evaluasi training.

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Training is one of the aspects regulated in GMP which is an important thing to be carried out and given by the pharmaceutical industry to each personnel to prepare qualified personnel. There is a need for documentation related to the training list for production operators which has not been well documented at PT. Darya-Varia Laboratoria Plant Gunung Putri. The method to create a matrix training plan was carried out by form a classification of the production section according to its application at PT. Darya Varia Laboratoria Plant Gunung Putri was then sorted and classified into SOPs and batch manufacturing records as the basis for the training. The last step was the preparation of training materials along with training evaluation form supplemented by an operator qualification matrix according to the results of the training evaluation carry out. The results of the preparation and formation of the matrix training plan for the general pharmacy section obtained 83 training plans for the mixing section, 73 training plans for the filling, and 33 training plans for the tulle production, while for the soft capsule section, 58 training plans for the gelatin section, 62 training plans for mixing and compounding, 63 training plans for encapsulation, 49 training plans for inspection and drying, 56 training plans for sorting and printing, 52 training plans for polishing, and 59 training plans for striping. The resulting training evaluation form are 71 sections with consisting of 10 to 20 questions and operator qualification criteria based on the training evaluation value."

"Pesatnya perkembangan teknologi telah mengubah perdagangan konvensional menjadi sistem perdagangan modern. Agar e-commerce berhasil harus dikembangkan menggunakan sistem yang akurat. Salah satu metode pada pendekatan collaborative filtering yaitu latent variable models berdasarkan faktorisasi matriks. Jika setiap vector pu yang menyatakan ketertarikan pengguna ke-u terhadap variabel tersembunyi dan setiap vector qi yang menyatakan hubungan item i dengan variabel tersembunyi dapat ditentukan, maka tingkat ketertarikan antara semua pengguna u pada setiap item i dapat ditentukan. Untuk menghindari terjadinya overfitting proses update pu dan qi dilakukan menggunakan metode gradient descent dengan regularisasi. Penelitian ini menentukan parameter k (banyaknya variabel tersembunyi) dan parameter (nilai regularisasi) agar model optimal.

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The rapid development of technology has changed the conventional trade into a modern trading system. In order for successful e-commerce must be developed using an accurate system. One method in collaborative filtering approach that is latent variable models based on matrix factorization. If any vector pu that expressed interest u user to a hidden variable and each qi vector expressing the relation item i with hidden variables can be determined, then the level of interest among all users u on every item i can be determined. To avoid overfitting the update process on pu vector and qi vector performed using gradient descent method with regularization. This study determines the parameter k (the number of hidden variables) and parameter (value regularization) that makes the model becomes optimal."

"Matrix analytic methods are popular as modeling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. In the current literature, a mixed bag of techniques is used-some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of the matrix analytic approach are included. The authors begin by describing several examples of quasi-birth-and-death (QBD) processes. These examples give the reader an idea of the variety of models which are hidden by the general block notation as well as reinforce some of the terminology and notation used throughout the text. These same examples are used as illustrations later. The second part of the book deals with phase-type distributions and related-point processes, which provide a versatile set of tractable models for applied probability. Part three reviews birth-and-death processes, and points out that the arguments for these processes carry over to more general processes in a parallel manner and are based on Markov renewal theory. Part four covers material where algorithmic and probabilistic reasoning are most intimately connected. In three steps, the authors take you from one of the simplest iterative procedures to the fastest, relating the successive approximations to the dynamic behavior of the stochastic process itself. The final part goes beyond simple QBDs with a sequence of short chapters where the authors discuss various extensions to the analyzed processes. Their intention is to show that the fundamental ideas extend beyond simple homogeneous QBD."

"Pada penelitian ini zeolite-A digunakan sebagai matriks pembawa aroma yang menahan laju pelepasan minyak atsiri mawar (Rosa damacena Mill.) yang dapat diregenerasi. Zeolite-A disintesis dari kaolin Bangka Belitung menggunakan metode hidrotermal yang terdiri dari proses metakaolinisasi dan zeolitisasi. Zeolite-A dengan 20 wt% bentonite dicampur untuk membentuk matriks ZAB. Bentonite berfungsi sebagai bahan pengikat yang memiliki kemampuan adsorpsi minyak atsiri sebesar 1,497 g/g bentonite. Zeolite-A dan matriks ZAB dikarakterisasi menggunakan X-Ray Difraction, Brunauer–Emmett–Teller, Fourier-transform infrared spectroscopy, Scanning Electron Microscopy- Energy Dispersive X-Ray Spectroscopy. Pengaruh aktivasi kimia zeolite-A terhadap kinerja adsorpsi matriks ZAB diamati dengan penggunaan zat aktivator berbeda, yaitu HCl 0,1 M dan NaOH 0,1 M. Pengamatan siklus regenerasi dilakukan sebanyak 10 kali. Jumlah minyak atsiri teradsorpsi per berat matriks diamati dengan analisis gravimetrik. Tanpa aktivasi kimia, matriks ZAB dengan diameter 0,4; 0,7; 1 cm dapat mengadsorpsi minyak atsiri masing-masing sebesar 1,807; 1,624; 1,411 g/g matriks. Matriks ZAB diameter 0,4 cm teraktivasi HCl 0,1 M dan NaOH 0,1 M berturut-urut mampu mengadsorpsi minyak atsiri mawar sebanyak 1,95 dan 1,807 g/g matriks. Hasil tersebut mengindikasikan aktivasi dengan HCl 0,1 M mampu memperbesar pori sehingga minyak atsiri semakin banyak teradsorbsi. Hingga minggu ke-5 matriks ZAB masih mengandung geraniol, feniletil alkohol, linalool, sitral, sitronellol dan eugenol dengan laju pelepasan masing-masing senyawa adalah 0,04; 0,07; 0,037; 0,021; 0,026; dan 0,011 g/minggu. Hasil ini menunjukkan pelet matriks berbasis zeolite-A mampu menahan pelepasan aroma pada minyak atsiri mawar lebih dari satu bulan

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In this study zeolite-A used as a fragrance carrier matrix which retained the rate of release of rose essential oil (Rose damacena Mill.) which can be regenerated. Zeolite-A was synthesized from Bangka Belitung kaolin using hydrothermal method which consists metakaolinization and zeolitization processes. Zeolite-A and 20 wt% bentonite are mixed to form ZAB matrix. Bentonite functiona as matrix binder which can adsorb rose essential oil 1,497 g/g bentonite. Zeolite-A and ZAB matrix was characterized using X-Ray Difraction, Brunauer–Emmett–Teller, Fourier-transform infrared spectroscopy, Scanning Electron Microscopy-Energy Dispersive X-Ray Spectroscopy. Observation of chemical activation effect on zeolite-A was carried out by using different activator substances, HCl 0.1 M and NaOH 0.1 M. Observation of regeneration cycle was carried out 10 times. The amount of essential oil adsorbed per matrix weight was observed by gravimetric analysis. Without chemical activation, ZAB matrix with a diameter of 0.4; 0.7; 1 cm each has the ability to adsorb essential oils 1.807; 1.624; 1.411 g/g matrix. The 0,4 mm ZAB matrix activated with HCL o.1 M and NaOH 0.1 M each has the ability to adsorb rose essential oil 1,95 and 1,807 g/g matrix, respectively. These results indicate that activation using HCl 0.1 M enlarge pores and allow matrix to adsorb more rose essential oil. Slow release of rose essential oil observed using Gas Matrix pellet still contained geraniol, phenylethyl alcohol, linalool, citral, citronellol and eugenol on the fifth week with release rate of 0.04; 0.07; 0.037; 0.021; 0.026; and 0.011 g/week, respectively. This result shows that zeolite-A-based matrix pellets are able to withstand the release of aroma in rose essential oil up to more than a month."

"Suatu ruang metrik dikatakan ruang Atsuji jika setiap fungsi kontinu bernilai riil di ruang tersebut merupakan fungsi kontinu seragam. Ruang Atsuji merupakan ruang metrik yang lengkap. Ruang metrik dikatakan memiliki Atsuji completion jika completion-nya adalah ruang Atsuji. Tujuan skripsi ini adalah mempelajari dan menjelaskan syarat-syarat suatu barisan di ruang metrik yang memiliki Atsuji completion agar barisannya memiliki subbarisan Cauchy. Barisan yang ditinjau merupakan barisan pseudo-Cauchy, barisan asimtotik, barisan dari titik akumulasi, dan barisan dari pasangan titik terisolasi.

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A metric space is called an Atsuji space if every real-valued continuous function on it is uniformly continuous. An Atsuji space is a complete space. A metric space is said to have an Atsuji completion if its completion is an Atsuji space. The aim of this undergraduate thesis is to study and explain the condition of sequences in metric space which has Atsuji completion in order to have a Cauchy subsequence. The sequences being considered are pseudo-Cauchy sequence, asymptotic sequence, sequence of accumulation points, and sequence of paired isolated points."

"ABSTRAKSecara umum penyembunyian data (steganografi) dengan media penampung citradigital terdiri dari dua teknik yaitu spasial domain dan frekuensi domain. Salahsatu metode yang menggunakan teknik spasial domain adalah pixel valuedifferencing (PVD). PVD menghitung selisih nilai pixel yang bersebelahan dengannon-overlapping. Misalkan data berhasil disisipkan tanpa menggunakan semuapixel dari cover image maka pada proses ekstraksi pesan mengalami penambahansehingga diperlukan suatu penanda untuk menjamin kesesuaian pesan. PVDmembutuhkan proses kuantisasi yang merepresentasikan prinsip kapabilitas visualmata manusia yaitu area kontras dan area mulus sehingga nilai selisih pixel yangbaru interval nilainya sama dengan interval selisih nilai pixel awal. Salah satumetode untuk kuantisasinya yakni menggunakan metode perfect square number.Pada skripsi ini mengimplementasikan PVD ditambahkan penanda dengan perfectsquare number dalam mengamankan data dengan citra digital. Hasil simulasiterhadap data uji dianalisis berdasarkan rata-rata waktu proses yang menunjukkansemakin besar ukuran media penampung maka semakin lama waktu yangdiperlukan dan nilai Peak Signal to Noise Ratio (PSNR) berada di interval 50 dBsampai 86 dB yang mengindikasikan bahwa pesan rahasia yang disembunyikansulit terdeteksi.

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ABSTRACTIn general, data hiding with cover is image consists of two techniques; spatialdomain and frequency domain. One method using spatial domain technique is thepixel value differencing (PVD). PVD calculates the difference between pixels andnon-overlapping. If the data was able to be attached without using all the pixelsfrom cover image, then the message extraction process will expand, which makesthe sign is needed to guarantee the suitability of the message. PVD requiresquantitative processes representing the principal of human visual system capabilitywhich are contrast areas and smooth areas with the result that the new pixeldifference value has the same value interval as the initial pixel difference value.One of the methods for the quantitation is using perfect square number. Thisundergraduate thesis implements the PVD and perfect square number in securingdata by digital image. The simulation results of the test data analyzed based onaverage processing time shows that the bigger value of image pixel, the longertime required and the value of PSNR is in the interval 50 dB to 85 dB indicatingthe secret message that is hidden difficult to be detected."

"Pencacahan clique maksimal adalah suatu metode graph clustering yang bertujuan untuk mencari simpul mana saja yang memiliki peranan paling besar dalam suatu graf. Pencacahan clique maksimal ini telah banyak diaplikasikan, diantaranya analisis pada jaringan sosial, pendeteksian hierarki melalui jaringan email, analisis statistik jaringan finansial, clustering pada jaringan dinamis, dan komputasi biologi. Algoritma Bron-Kerbosch merupakan salah satu algoritma tercepat dalam pencarian clique maksimal, maka pada penelitian ini, digunakanlah algoritma Bron-Kerbosch. Dalam mencacah semua clique maksimal dari suatu graf, matriks yang biasa digunakan adalah matriks ketetanggaan dari graf tersebut, sehingga dapat diperoleh simpul mana saja pada graf yang memiliki peranan paling besar. Selain matriks ketetanggaan, penelitian ini juga menggunakan matriks komplemen dalam mencacah clique maksimal. Data yang digunakan dalam penelitian ini adalah graf yang merepresentasikan rute jalur penerbangan domestik dari salah satu maskapai penerbangan di Indonesia. Dengan menerapkan algoritma Bron-Kerbosch, semua clique maksimal dari graf terkait akan didaftar, sehingga dapat diperoleh simpul yang memiliki peranan paling besar dalam graf ini. Graf tersebut direpresentasikan dalam bentuk matriks ketetanggaan dan juga matriks komplemen. Hasil penerapan algoritma Bron-Kerbosch pada data, baik yang menggunakan matriks ketetanggaan maupun matriks komplemen, keduanya memberikan hasil yang sama dalam menentukan simpul yang memiliki peranan paling besar dari graf terkait. Selain itu, melalui hasil penerapan yang menggunakan matriks komplemen, dapat diketahui pula simpul-simpul yang hanya bertetangga langsung dengan simpul yang memiliki peranan paling besar.

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Maximal clique enumeration is a graph clustering method for finding all vertices that have the most influence in a graph. This maximal clique enumeration has largely been applied, including social network analysis, hierarchy detection through email networks, statistical analysis of financial networks, clustering in dynamic networks, and computational biology. The Bron-Kerbosch algorithm is one of the fastest algorithms to find all maximal cliques, hence this research will focus on that algorithm to find all maximal cliques. Counting all maximal cliques of a graph usually uses an adjacency matrix of the graph to find all vertices in the graph that have the most influence. Other than adjacency matrix, this research will also use a complement matrix in counting all maximal cliques. This research uses a graph that represents a domestic flight route of one of the airlines in Indonesia. By using Bron-Kerbosch algorithm, all maximal cliques of the graph will be listed, so that it will come up with the vertices which are the most influential in this graph. The graph will be represented in an adjacency matrix as well as a complement matrix. The result of applying the Bron-Kerbosch algorithm both the adjacency and the complement matrix?will give the same result in determining vertices that have the most influence in the graph. Besides that, by using a complement matrix, the result gives more information on the vertices which are only connected to the vertices that have the most influence."

"Suatu ruang metrik disebut ruang Atsuji jika untuk setiap fungsi bernilai real yang kontinu adalah kontinu seragam. Ruang metrik dikatakan memiliki Atsuji completion jika completion dari ruang metrik tersebut adalah ruang Atsuji. Dalam skripsi ini dibahas syarat subhimpunan lengkap di ruang metrik agar ruang metriknya memiliki Atsuji completion. Ruang metrik yang ditinjau adalah ruang metrik yang himpunan titik akumulasinya adalah himpunan yang terbatas total (totally bounded).

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A metric space is called an Atsuji Space if every real-valued continuous function on it is uniformly continuous. A metric space is called to have an Atsuji completion if its completion is an Atsuji space. This skripsi discuss the conditions of complete subset in metric space in order to have an Atsuji completion. The metric space being considered is a metric space which has a totally bounded accumulation point set."