Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure

PENGEMBANGAN MODUL PEMBELAJARAN PADA STANDAR KOMPETENSI MENERAPKAN DASAR-DASAR KELISTRIKAN DI SMK NEGERI 2 BOJONEGORO

Abstrak Observasi yang dilakukan peneliti menujukkan bahwa di SMK Negeri 2 Bojonegoro siswa memang mempunyai modul pembelajaran tetapi modul yang digunakan belum sesuai dengan potensi siswa dan kurang sesuai dengan standar modul, jadi secara umum penelitian ini bertujuan untuk mengetahui potensi siswa di SMK Negeri 2 Bojonegoro, kualitas modul pembelajaran, dan hasil belajar siswa. Penelitian ini termasuk penelitian pengembangan, karena dalam penelitian ini dikembangkan modul dan perangkat pembelajaran. Pengembangan modul pembelajaran ini mengacu pada pengembangan 4D (Define, Design, Develop, and Disseminate). Subyek penelitian ini adalah 32 siswa kelas X TEI 1. Rancangan uji coba yang digunakan untuk pengambilan data adalah desain penelitian eksperimen One Group Pretest Postest dengan hasil sebagai berikut: 1) dari hasil tes kemampuan penalaran formal diperoleh kesimpulan bahwa rata-rata siswa berada pada tingkat kemampuan penalaran transisi, 2) dari hasil validasi diperoleh 80,2% untuk modul pembelajaran dan 80% untuk butir soal maka dapat disimpulkan bahwa dapat/ layak digunakan, 3) diperoleh rata-rata nilai postest 64,62 dan standar deviasi 12,05 kemudian untuk pretest dengan nilai rata-rata 58,56 dan standar deviasi 12,20. Perbedaan antara hasil belajar tersebut dinyatakan taraf signifikan yakni sebesar 5%, untuk thitung sebesar 3,188 sedangkan nilai ttabel sebesar 2,04, jadi nilai thitung > ttabel dan pada probabilitas diperoleh P Value sebesar 0,003 maka P-Value < 0,05 dimana dapat dikategorikan H1 diterima dan H0 ditolak, dari pernyataan tersebut bahwa hasil belajar siswa setelah menggunakan modul pembelajaran meningkat dibandingkan dengan siswa sebelum menggunakan modul pembelajaran. Saran dari peneliti adalah dalam pengembangan modul hendaknya tidak hanya pada standar kompetensi menerapkan dasar-dasar kelistrikan saja diharapkan pengembangan modul bisa menyeluruh untuk semua standar kompetensi agar dapat membantu siswa dalam pembelajaran, dan pengembangan modul selanjutnya diharapkan memberikan konsep yang lebih bagus dan lebih menarik siswa untuk lebih menyenangi melakukan pembelajaran sendiri dengan modul agar meningkatkan hasil belajar. Kata kunci: Pengembangan Modul Pembelajaran dan Hasil Belajar. Abstract Observations conducted by researchers showed that in SMK Negeri 2 Bojonegoro student learning is having a module but the module is not used in accordance with the potential students and less according to the standard module, so generally, this study aims to determine the potential of students in SMK Negeri 2 Bojonegoro, quality learning modules, and student learning outcomes. This research development, because in this study developed learning modules and devices. This learning module development refers to the development of 4D (Define, Design, Develop, and Disseminate). The study subjects were 32 students of class X TEI 1. The design of experiments used for data retrieval experimental research design One Group Pretest Posttest with the following results: 1) the results of formal reasoning ability tests concluded that the average student there is at the level of reasoning ability transition, 2) the validation of results result obtained 80,2% for the learning modules and 80% for items we can conclude for use, 3) the result an average value and standard deviation of posttest 64,62 then 12,05 to pretest with an average value of 58,56 and a standard deviation of 12,20. The difference between the results of the study revealed that a significant level of 5%, the value of tcount 3,188 while the value of ttabel 2,04, so the value of tcount > ttable and the probabilities obtained the P Value 0,003, P-Value <0.05 which can be categorized H1 is accepted and H0 is rejected, from the statement that the learning outcomes of students after using the learning modules increased compared with students before using the learning modules. Keywords : Development of Learning Module and learning outcomes

PERBEDAAN HASIL BELAJAR SISWA antara MODEL PEMBELAJARAN GUIDE DISCOVERY dengan TEKNIK RESUME KELOMPOK dan MODEL PEMBELAJARAN GUIDE DISCOVERY di KELAS X TKJ SMK NEGERI 2 LAMONGAN

Abstrak Penelitian ini bertujuan untuk mengetahui apakah hasil belajar siswa pada kelas yang menggunakan model pembelajaran guide discovery dengan teknik resume kelompok lebih baik dari kelas yang menggunakan model pembelajaran guide discovery pada standar kompetensi melakukan perbaikan dan setting ulang sistem PC. Dalam penelitian ini  menggunakan salah satu desain penelitian eksperimen yaitu Quasi Experimen Design (Nonequivalent control group design). Pengumpulan data dalam penelitian ini diperoleh melalui tes hasil belajar (LP2, LP3, pre-test dan post-test). Prosedur dalam penelitian ini, yaitu tahap persiapan dan perencanaan penelitian, tahap pelaksanaan, dan tahap akhir. Dari hasil penelitian yang diperoleh,menunjukkan bahwa: (1) rata-rata hasil belajar kelas X-TKJ 1 adalah sebesar 85,1 dengan standar deviasi sebesar 1,048 dan rata-rata hasil belajar kelas X-TKJ 2 adalah sebesar 81 dengan standart deviasi 2,769 daan hasil perhitungan uji mann-whitney u test didapat p  0,05, yaitu nilai probabilitas pada taraf signifikansinya 5% (0,05) adalah p = 0,000, (2) dilihat bahwa rata-rata respon siswa secara keseluruhan yang menjawab sangat setuju sebesar 40%, setuju 49%, dan cukup setuju 11%, sehingga respon siswa terhadap pembelajaran guide discovery dengan teknik resume kelompok dikatakan positif. Berdasarkan hasil penelitian di atas, maka dapat disimpulkan bahwa hasil belajar siswa pada kelas yang menggunakan model pembelajaran guide discovery dengan teknik resume kelompok lebih baik dari kelas yang menggunakan model pembelajaran guide discovery pada standar kompetensi melakukan perbaikan dan setting ulang sistem PC. Harapan yang dapat peneliti sampaikan, hendaknya model pembelajaran guide discovery dengan teknik resume kelompok dapat dikembangkan dan digunakan dalam proses belajar mengajar dengan sebelumnya melakukan telaah kompetensi yang ingin dicapai sehingga penerapannya sesuai dengan kompetensi yang ingin dicapai sehingga mendapatkan  hasil yang  lebih maksimal.   Kata kunci: Model pembelajaran guide discovery dengan teknik resume kelompok, model pembelajaran guide discovery, hasil belajar siswa. Abstract This study aims to determine whether student learning result in the classroom using guide discovery model with a group resume technique is better than classroom using guide discovery model standards of competence make improvements and re-setting the PC system. In this research using one of the experimental research design that is Quasi Experiment Design (Nonequivalent control group design). Collecting data in this study was obtained through achievement test (LP2, LP3, pre-test and post-test). The procedures in this study, the preparation and planning stage of the research, implementation phase, and the final stage. From the research results obtained, shows that: (1) an average of the results of studying class X-TKJ 1 is at 85,1 with a standard deviation of 1,048 and the average of the results of studying class X-TKJ 2 is at 81 with a standard deviation of 2,769 and the results of Mann-Whitney test calculations u test obtained p  0.05, probability value at 5% significance level (0.05) is p = 0.000, (2) shows that the average overall response of students who answered 40% strongly agree, 49% agree and 11% agree enough, so that the students' response to the guide discovery with group resume technique is said to positive. Based on the above results, it can be concluded that there is a difference in student learning result in the classroom using guide discovery model with a group resume technique is better than classroom using guide discovery model standards of competence make improvements and re-setting the PC system. Hope that researchers can tell, should be a discovery learning model with group resumes techniques can be developed and used in teaching and learning by doing research previous competencies to be achieved so that the application in accordance with the competencies to be achieved so as to get maximum results. Keywords: Guide discovery model with groups resume technique, Guide discovery model, student learning result

PERBANDINGAN HASIL BELAJAR SISWA ANTARA METODE PEMBELAJARAN SNOWBALL THROWING DAN METODE PEMBELAJARAN COURSE REVIEW HOREY (Pada Mata Pelajaran Sistem Komputer di SMK Negeri 3 Buduran)

Abstrak Penelitian ini bertujuan untuk mengetahui apakah hasil belajar siswa yang menggunakan metode pembelajaran snowball throwing lebih baik dari metode pembelajaran course review horey, maka peneliti melakukan penelitian dengan menggunakan metode pembelajaran snowball throwing dan metode pembelajaran course review horey pada mata pelajaran sistem komputer  . Metode yang digunakan adalah quasi experiment dengan rancangan penelitian yang digunakan yaitu “Non Equivalen Control Design”. Populasi dalam penelitian ini adalah siswa kelas X TKJ SMKN 3 Buduran. Diambil sampel sebanyak 2 kelas, kelas X TKJ 1 sebagai kelas eksperimen dan X TKJ 2 sebagai kelas kontrol. Sedangkan untuk mengetahui perbedaan hasil belajarnya digunakan teknik analisis data uji-t. Hasil penelitian menunjukkan bahwa hasil pretest pada siswa sebelum menggunakan metode pembelajaran snowball throwing sama rendah dengan hasil belajar siswa sebelum menggunakan metode pembelajaran course review horey. Hasil posttest menunjukkan bahwa siswa yang menggunakan metode pembelajaran snowball throwing memiliki hasil belajar lebih tinggi dibandingkan dengan hasil belajar siswa yang menggunakan metode pembelajaran course review horey. Dengan rata-rata hasil belajar kelas eksperimen (X TKJ 1) adalah 91,3 dan rata-rata hasil belajar kelas kontrol (X TKJ 2) adalah 84,8 serta diperoleh thitung = 3,129 > ttabel = 1,67 dengan taraf signifikansi sebesar 5%. Ini menunjukkan bahwa perbandingan metode pembelajaran snowball throwing lebih baik dibandingkan dengan metode pembelajaran course review horey. Penerapan metode pembelajaran snowball throwing dan metode pembelajaran course review horey dapat digunakan sebagai inovasi baru dalam pembelajaran dalam rangka menuntaskan hasil belajar siswa, sehingga pendekatan ini dapat diterapkan pada mata diklat lain yang sesuai.   Kata kunci     : metode pembelajaran snowball throwing, metode pembelajaran course review horey, hasil belajar siswa, respon siswa. Abstract This research aimed to know the whether of student learning achievement which used snowball throwing instruction method better than course review horey instruction method. Researcher conducting this research by using snowball throwing instruction method and course review horey instruction method on lesson of Computer System. Method used was quasi experiment with research design “Non Equivalent Control Design”. The population in this research was students in grade X TKJ SMKN 3 Buduran. Samples taken were 2 classrooms, X TKJ 1 as experiment classroom and X TKJ 2 as control classroom. To know the differences of learning achievement it was used t-test analysis technique. Yield of the research shows that pretest achievement of student before using snowball throwing instruction method was as low as course review horey instruction method. Posttest result shows that students which used snowball throwing instruction method have learning achievement higher than students which using course review horey instruction method. The average learning achievement of experiment classroom (X TKJ 1) was 91.3 and average learning achievement of control classroom (X TKJ 2) was 84,8 also obtained tcalculation = 3.129 > ttable = 1.67 with significance degree 5%. These is shows that the comparison of snowball throwing instruction method better than course review horey instruction method. The application of learning methods snowball throwing and learning methods horey course reviews can be used as a new innovation in learning in order to complete the learning outcomes of students, so this approach can be applied to another kind appropriate of training.   Keyword : snowball throwing instruction method, course review horey instruction method, students learning achievement, student respons

PENGEMBANGAN PERANGKAT PEMBELAJARAN DENGAN MENGGUNAKAN MODEL PROBLEM-BASED INSTRUCTION DAN PEMBENTUKAN KARAKTER ENTREPRENEUR PADA MATA PELAJARAN TEKNIK ELEKTRONIKA DASAR DI SMKN 1 SIDOARJO

Abstrak Tujuan dari penelitian ini adalah untuk menghasilkan perangkat pembelajaran yang layak, melatihkan nilai-nilai karakter entrepreneur serta mengetahui ketuntasan belajar siswa yang meliputi pengetahuan dan ketrampilan, dan mengetahui respon siswa terhadap pembelajaran mata pelajaran teknik elektronika dasar. Penelitian ini dilakukan melalui pengembangan perangkat pembelajaran dengan menggunakan model problem-based instruction dan pembentukan karakter entrepreneur pada mata pelajaran teknik elektronika dasar dengan mengacu model pengembangan model instructional development cycle, selanjutnya menguji cobakan perangkat pembelajaran pada 32 siswa Kelas X TAV  SMK Negeri 1 Sidoarjo. Rancangan dalam uji coba menggunakan one-group pretest-postest design. Temuan hasil penelitian yakni perangkat pembelajaran dengan menggunakan model problem-based instruction dan pembentukan karakter entrepreneur yang terdiri dari silabus, Rencana Pelaksanaan Pembelajaran (RPP), Lembar Kerja Siswa (LKS) dilengkapi Kunci LKS, dan Lembar Penilaian (LP) dilengkapi dengan Kunci LP dikategorikan baik. Nilai-nilai karakter entrepreneur siswa diantaranya mandiri, jujur, tidak kreatif, inovatif, komunikatif, dan tanggung jawab memperoleh nilai kompetensi baik. Persentase ketuntasan belajar pengetahuan siswa sebesar 87,5%, persentase ketuntasan ketrampilan proses siswa sebesar 100%, sedangkan persentase ketuntasan belajar ketrampilan psikomotor siswa sebesar 100%. Respon siswa sangat tertarik dan senang dalam pembelajaran. Kata-kata kunci: model problem-based instruction, pembentukan karakter entrepreneur. Abstract The purpose of this research are to get a proper learning equipment, to train the entrepreneur character and to know the students learning completeness that includes knowledge and skill, and to know learning completeness on basic electronics subject. This research is done the development using a model of learning problem-based instruction and character building entrepreneurs on basic electronics engineering subjects refers to development model of instructional development cycle, and the testing learning equipments on 32 students of class X  TAV SMK Negeri 1 Sidoarjo. The design of the test is using a one-group pretes-posttest design. The result of this research are learning equipment study using a model of problem-based instruction and building character entrepreneurs which consists of syllabus, lesson plan, student worksheets include key worksheets and assessment sheet include well categorized key of assessment sheet. Character values of students such as independent, honest, creative, innovative, communicative, and respect get a good competence in value. The percentage of students learning completeness of knowledge is 87,5%, the pecentage of students completeness of skill is 100%, while the percentage of students learning completeness of phychomotor skill is 100%. Student response was very interested and excited in learning. Keywords: model of problem-based instruction, building character entrepreneurs

PENGARUH MODEL PEMBELAJARAN PROBLEM SOLVING SEARCH, SOLVE, CREATE, AND SHARE TERHADAP HASIL BELAJAR SISWA SMK PADA MATA PELAJARAN TEKNIK ELEKTRONIKA DASAR

Abstrak Penelitian ini bertujuan untuk mengetahui hasil belajar dan aktivitas belajar siswa dengan model pembelajaran problem solving search, solve, create, and share dibandingkan dengan model pembelajaran konvensional pada mata pelajaran teknik elektronika dasar di kelas X TAV SMK Negeri 2 Surabaya. Hasil belajar dan aktivitas siswa tersebut dibandingkan untuk mengetahui model pembelajaran dengan hasil yang terbaik. Jenis penelitian yang digunakan dalam penelitian ini adalah Jenis penelitian eksperimen. Desain penelitian yang digunakan adalah Nonequivalent Control Group Design yang termasuk kategori Quasi Experimental Design. Pengambilan sampel untuk kelas eksperimen dan kelas kontrol tidak dipilih secara acak, Kelas eksperimen menggunakan model pembelajaran problem solving search, solve, create, and share, sedangkan untuk kelas kontrol menggunakan model pembelajaran konvensional. Data penelitian berupa hasil belajar siswa diambil dengan teknik tes yang berupa pilihan ganda dan uraian. Hasil penelitian dan analisis data menunjukkan bahwa model pembelajaran problem solving search, solve, create, and share lebih baik dibandingkan model pembelajaran konvensional. Hal tersebut dibuktikan dengan hasil uji-t dimana t hitung > t tabel dengan taraf signifikansi α = 0,05 yakni hasil belajar kelas eksperimen diperoleh t hitung sebesar 2,78 dan t tabel sebesar 1,67 dan siswa yang menggunakan model pembelajaran problem solving search, solve, create, and share lebih aktif dibandingkan model pembelajaran konvensional yaitu sebesar 85,30% untuk kelas eksperimen dan 77,08% untuk kelas kontrol. Kata Kunci: Model pembelajaran problem solving search, solve, create, and share, Model pembelajaran konvensional, Hasil belajar siswa. Abstract This research aims to find out differences of student achievement and student learning activities, for student with  problem solving learning model type search, solve, creat and share compared by conventional learning model in basic of electronics subject in X TAV Classroom of SMK Negeri 2 Surabaya. both of student achievement and student learning activities are compared to determine which one the learning models with the best result. This research used experiments of research. The design is a nonequivalent control group design that included the category of Quasi Experimental Design. Sampling for the experimental class and the control class, not randomly chosen, the experimental class of problem solving learning model type search, solve, create, and share, while for control class using conventional learning models. Research data were taken in the form of student learning achievement with techniques test such as multiple-choice tests and descriptions. The results of the research and analysis of the data shows that the problem solving learning models type search, solve, create, and share better than conventional learning models. This is evidenced by the results of t-test where t count > t table with a significance level α = 0.05 the student achievement in experimental class obtained  2.78 for t count and 1.67 t table and student with problem solving learning models type search, solve, create, and share more active in learning than the student with conventional learning models, its determine by 85,30% for experiment class and 77,08% for control class. Keywords: Problem solving learning models type search, solve, create, and share, conventional learning models, student achievement

Pengaruh Model Pembelajaran dan Motivasi Berprestasi terhadap Hasil Belajar Siswa pada Materi Ms Excel

This research was aimed to know the influence of learning outcome of students using direct learning model and the learning outcome of students using cooperative learning model – Student Teams Achievement Divisions (STAD) type - on IF logic function. The method used in this research was quasi experiment with Non-equivalent control group design model. The research was held at XI-IA1 class ( using direct learning model) and XI-IA6 (using cooperative learning model type STAD). Choosing the two researched classes was based on random sampling technique. The research design used two way – anova. The instrument used was an objective test ( 7 items) which its validity and reliability had been tested. According to the data analysis, we knew that: (1) There was a different of the learning outcome between the students taught using direct learning model and the ones taught using cooperative learning model – type STAD. This conclusion was based on the result of the hypothesis testing to the two classes - post test score namely; thit 3.983 > ttabel 1.69 or (Fhit) 76.190 > 0.073 (sig.), at significant 0.05. (2) There was no different of the learning outcome between the students who had high achieving motivation and the ones had low one. This conclusion was shown by the result of the hypothesis testing, thit 0.259 < ttable 1.69 or (Fhit) 0.026 < 0.899 (sig.), at significant 0.05. (3) There was a correlation between a learning model and students\u27 achieving motivation. This conclusion was proved by the result of the probability testing Fhit 0.129 < Ftable 0.169, or Fhit 0.129 < 0.720(sig.) at significant 0.05

Chemical recycling of polyethylene terephthalate (PET) to monomers: Mathematical modeling of the transesterification reaction of bis(2-hydroxyethyl) terephthalate to dimethyl terephthalate

The accumulation of plastic waste in the environment is making recycling a compelling issue, particularly for polyethylene terephthalate (PET), used in products with a short shelf-life. An appealing route to chemical recycling of PET is glycolysis, leading to bis(2-hydroxyethyl) terephthalate (BHET). Its subsequent transesterification with methanol to dimethyl terephthalate (DMT) is crucial for the recovery of polymer-grade monomers. To favor the industrial applicability of this process, this work investigates the influence of three main parameters, i.e. the methanol to ethylene glycol molar ratio, the solvent to oligomers molar ratio and the mass fraction of the catalyst, on the transesterification of BHET to DMT. A kinetic model has been proposed, and the reaction rates evaluated by comparison with the experimental data. The model was used to predict the performances of the process in a wide range of operating conditions, in order to establish the optimal ones for high yield to DMT

A computational framework for two-dimensional random walks with restarts

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in [D. A. Bini, S. Massei, and B. Meini, Math. Comp., 87 (2018), pp. 2811-2830] which allows us to deal with more general situations such as processes involving restart events. This is motivated by the need for modeling processes that can incur in unexpected failures like computer system reboots. We present a theoretical analysis of an enriched Banach algebra that, combined with appropriate algorithms, enables the numerical treatment of these problems. The results are applied to the solution of bidimensional quasi-birth-death processes with infinitely many phases which model random walks in the quarter plane, relying on the matrix analytic approach. The reliability of our approach is confirmed by extensive numerical experimentation on several case studies