Keterbatasan Operator Integral Tentu Dan Operator Riemann-Liouville Di Ruang Lebesgue Terboboti

Paper ini membahas keterbatasan operator integral tentu dan perumumannya yang kemudian disebut operator Riemann-Liouville di ruang Lebesgue terboboti. Dalam hal ini, pembuktian keterbatasan operator-operator tersebut menggunakan ketaksamaan Holder dan Minkowski. Dengan menggunakan fakta bahwa operator integral tentu adalah operator yang terbatas di ruang Lebesgue terboboti diperoleh hasil tentang terbatasnya operator Riemann-Liouville di ruang Lebesgue terboboti. Kata kunci: Operator integral tentu, Operator Riemann-Liouville, ruang Lebesgue, ruang Lebesgue terboboti

The Role of Quorum Sensing in Bacterial Colony Dynamics

The quorum sensing (QS) signalling system allows colonies of bacteria to coordinate gene expression to optimise behaviour at low and high cell densities, giving rise to individual and group responses, respectively. The main aim of this thesis is to understand better the important roles of QS in bacterial colony dynamics. Thus a mathematical description was developed to thoroughly explore key mechanisms and parameter sensitivity. The nature of the QS system depends very much on the species. Pseudomonas aeruginosa was chosen as a model species for this study. P. aeruginosa is a Gram-negative bacterium that is responsible for a wide range of chronic infections in humans. Its QS signalling system is known to involve the las, rhl and pqs systems; this thesis focuses on the first two. The las system includes the LasR regulator and LasI synthase, which direct the synthesis of autoinducer 3O-C12-HSL. Similarly, the rhl system consists of the RhlR regulator and RhlI synthase, directing the synthesis of autoinducer C4-HSL. The mathematical model of the las system displays hysteresis phenomena and excitable dynamics. In essence, the system can have two stable steady states reflecting low and high signal molecule production, separated by one unstable steady state. This feature of the las system can give rise to excitable pulse generation with important downstream impact on the rhl system. The las system is coupled to the rhl system in two ways. First, LasR and 3O-C12-HSL activate the expression of their counterpart in the rhl system. Second, 3O-C12-HSL blocks activation of RhlR by C4-HSL. Furthermore, the las-rhl interaction provides a `quorum memory' that allows cells to trigger rhamnolipid production when they are at the edge of colony. It was demonstrated how the dynamical QS system in individual cells and with coupling between cells can affect the dynamics of the bacterial colony

Pulse generation in the quorum machinery of Pseudomonas aeruginosa

Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quo- rum sensing (QS) to coordinate gene expressions, including virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involve multiple control components, notably the las, rhl and pqs systems. In this paper, we examine the las system and, in partic- ular, the repressive interaction of rsaL, an embedded small regulative protein, employing recent biochemical information to aid model construction. Using analytic methods we show how this feature can give rise to excitable pulse generation in this subsystem with important downstream consequences for rhamnolipid production. We adopt a symmetric competitive inhibition to cap- ture the binding in the lasI-rsaL intergenic region and show our results are not dependent on the exact choice of this functional form. Furthermore, we exam- ine the coupling of lasR to the rhl system, the impact of the predicted capacity for pulse generation and the biophysical consequences of this behaviour. We hypothesise that the interaction between the las and rhl systems may provide a quorum memory to enable cells to trigger rhamnolipid production only when they are at the edge of an established aggregation

Mathematical Modelling of Drug Abuse Reduction Strategies taking into account the Treatment Type and Risks Level

Drug abuse is one of the global issues and has spread among teenagers. Drugs may lead to subordination, health problems and even death. There are several policies made in each country related to the problem of drug abuse, both punishment and treatment. In this paper, we discuss the treatment and strategy to reduce the number of drug users. Drug users can recover themselves by undergoing rehabilitation in the form of inpatient or outpatient care. We first conduct qualitative analyses including stability analysis of equilibrium points of the model, the basic reproduction number and parameter sensitivity analysis. Mathematical model of drug abuse reduction by concerning type of treatment along with risk level without control has two equilibrium points, namely non-endemic or drug-free equilibrium and endemic equilibrium. Sensitivity analysis is provided to investigate which parameter that most affects the dynamical behaviour of the drug abuse model in terms of stability of the non-endemic and endemic equilibrium point. Then we impose an anti-drug campaign on the model as strategy control to reduce the number of drug abusers. Simulation results show that the anti-drug campaign has a significant effect in reducing both the number of drug abusers who received any treatment and do not get any treatment

PENINGKATAN KETERAMPILAN GURU MATEMATIKA SMP DALAM PENGELOLAAN DISTANCE LEARNING SEBAGAI PERLUASAN RAGAM PEMBELAJARAN DI KABUPATEN JEMBER

Pandemik Covid-19 yang terjadi pada tahun 2020 telah berdampak secara signifikan pada semua bidang, salah satunya bidang pendidikan. Guru tidak lagi bisa melakukan proses pembelajaran secara tatap muka di kelas. Oleh karena itu guru dituntut untuk dapat melakukan proses belajar mengajar secara daring. Pada kegiatan pengabdian kepada masyarakat ini bertujuan untuk meningkatkan keterampilan guru dalam mengelola distance learning menggunakan Moodle. Rangkaian kegiatan diawali dengan proses instalasi moodle, proses perancangan pembelajaran, pembuatan konten, pembuatan forum interaksi, serta manajemen pengelolaan (desain, fitur, dan lain-lain) serta evaluasi. Peserta pengabdian kepada masyarakat ini adalah guru Matematika SMP yang tergabung dalam MGMP Matematika wilayah barat Kabupaten Jember sebanyak 30 orang dan semuanya dapat mengikuti pelatihan dari awal sampai akhir. Selain itu, peserta mampu membuat dan mengembangkan e-learning beserta kontennya menggunakan Moodle. Lebih lanjut diperolah peningkatan ketrampilan dan pengetahuan guru dalam mengelola distance learning menggunakan Moodle sebesar 33,09 %

Two isolation treatments on the COVID-19 model and optimal control with public education

This study examines a COVID-19 mathematical model with two isolation treatments. We assume that isolation has two treatments: isolation with and without treatment. We also investigated the model using public education as a control. We show that the model has two equilibria based on the model without control. The basic reproduction number influences the local stability of the equilibrium and the presence of an endemic equilibrium. Therefore, the optimal control problem is solved by applying Pontryagin’s Principle. In the 100th day following the intervention, the number of reported diseases decreased by 85.5% when public education was used as the primary control variable in the simulations

PENINGKATAN PROFESIONALITAS GURU DALAM PENYUSUNAN EVALUASI BERBASIS THINKING ANALYSIS BAGI GURU MATEMATIKA

Kegiatan pengabdian kepada masyarakat ini bertujuan untuk meningkatkan kompetensi gurudalam menyusun instrumen evaluasi pembelajaran yang bermutu berbasis thinking analysis yaitupembuatan soal kategori High Order Thinking Skill (HOTS). Kegiatan ini diawali denganpelatihan penyusunan soal HOTS dengan peserta guru mata pelajaran matematika tingkat SMPyang tergabung dalam MGMP Matematika Kabupaten Jember sebanyak 56 orang. Kegiatanberikutnya adalah penyusunan soal oleh peserta didampingi oleh tim pelaksana pengmasdilanjutkan dengan proses telaah soal. Berdasarkan hasil pengabdian ini secara keseluruhanterlihat bahwa kemampuan guru dalam menyusun soal kategori HOTS masih perlu ditingkatkanbaik sisi penguasaan materi maupun teknis penyusunan soal yang baik. Kegiatan pelatihan inidiakhiri dengan evaluasi atas pelaksanaan kegiatan maupun hasil penyusunan soal oleh peserta.Evaluasi dilaksanakan terintegrasi dengan kegiatan rutin MGMP Matematika tingkat SMP diKabupaten Jember. Luaran kegiatan ini adalah laporan kegiatan, video kegiatan, serta bukukumpulan seluruh soal yang disusun peserta

PELATIHAN DAN PENDAMPINGAN PEMBUATAN MEDIA PROMOSI BERBASIS TEKNOLOGI INFORMASI TERHADAP PRODUK-PRODUK UNGGULAN DAERAH DAN OBJEK WISATA DI KABUPATEN LAMONGAN

Salah satu sebab rendahnya perkembangan potensi ekonomi daerah adalah kurang tersebarnya informasi terkait produk-produk unggulan dan wisata alam daerah pada masyarakat luas. Hal ini yang mendasari dilakukannya program pengabdian kepada masyarakat di desa Kranji. Kegiatan yang dilakukan meliputi pelatihan dan pendampingan pembuatan website sebagai media promosi produk-produk unggulan dan wisata daerah berbasis teknologi informasi. Melalui kegiatan ini, diharapkan dapat membantu penyebaran informasi terkait potensi daerah sehingga meningkankan pendapatan masyarakat. Kegiatan ini dilakukan dalam empat tahapan, yaitu: koordinasi, pelatihan, pendampingan, dan evaluasi. Keberhasilan pelatihan dievaluasi dari nilai pretest dan posttest peserta yang menunjukkan adanya peningkatan sebesar 25%. Selain itu, didapatkan output berupa website yang telah dibuat oleh peserta berisikan potensi-potensi desa Kranji. Hasil evaluasi terhadap materi, narasumber, dan fasilitas pelatihan juga menunjukkan respon positif dari peserta dengan nilai 4,3 dari skala 5

Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1 and endemic equilibrium tend to asymptotically stable if R0 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control

Dynamic analysis and optimal control of COVID-19 with comorbidity: A modeling study of Indonesia

Comorbidity is defined as the coexistence of two or more diseases in a person at the same time. The mathematical analysis of the COVID-19 model with comorbidities presented includes model validation of cumulative cases infected with COVID-19 from 1 November 2020 to 19 May 2021 in Indonesia, followed by positivity and boundedness solutions, equilibrium point, basic reproduction number (R0), and stability of the equilibrium point. A sensitivity analysis was carried out to determine how the parameters affect the spread. Disease-free equilibrium points are asymptotically stable locally and globally if R0 < 1 and endemic equilibrium points exist, locally and globally asymptotically stable if R0 > 1. In addition, this disease is endemic in Indonesia, with R0 = 1.47. Furthermore, two optimal controls, namely public education and increased medical care, are included in the model to determine the best strategy to reduce the spread of the disease. Overall, the two control measures were equally effective in suppressing the spread of the disease as the number of COVID-19 infections was significantly reduced. Thus, it was concluded that more attention should be paid to patients with COVID-19 with underlying comorbid conditions because the probability of being infected with COVID-19 is higher and mortality in this population is much higher. Finally, the combined control strategy is an optimal strategy that provides an effective guarantee to protect the public from the COVID-19 infection based on numerical simulations and cost evaluations