Strong Convergence of Generalized Resolvents

Let M and fLng be a linear, closed, densely defined operator and a sequence of linear, closed, densely defined operators in a Banach Space X respectively. We consider a sequence of generalized resolvents fRn(¸)g, where Rn(¸) = (Ln¡¸M)¡1M. In this paper, we will prove that the sequence fRn(¸)g is uniformly bounded in n and ¸ in any compact subset of a certain open set. Then we will concern with consideration on strong convergence of fRn(¸)g. Finally we will give a criterion for the sequence fRn(¸)g converges strongly.Keywords : generalized resolvent, uniformly bounded, strong convergenc

SECOND ORDER CONE (SOC) DAN SIFAT-SIFAT KENDALA SECOND ORDER CONE PROGRAMMING DENGAN NORMA 1

Pada makalah ini dikembangkan pengertian Second Order Cone (SOC) dan sifat-sifat kendala Second Order Cone Programming dengan Norma 1. Kata kunci: Second Order Cone (SOC), Second Order Cone Programming

KEKONVEKSKAN DAERAH FISIBEL SECOND ORDER CONE PROGRAMMING DENGAN NORMA 1

Pada makalah ini disampaikan kekonvekskan daerah fisibel Second Order Cone Programming dengan Norma 1. Kata kunci: daerah fisibel, Second Order Cone Programmin

THE ANALITICAL SOLUTIONS OF THE LINEAR TWO CHANNELS DISSIPATION MODEL

The analytical solutions of the linear two channels dissipation model are presented in various forms. First we analyze the particular solutions of this model. Then the model is transformed into the Telegrapher Equation and further into the Klein Gordon Equation for which various families of solutions are known. The Fourier Transform is applied on the Telegrapher Equation, yielding solutions in Fourier representation. Finally we apply the method ofcharacteristics to find solutions of the initial value problem.Keywords : hyperbolic system, partial differential equation, exact solutio

EKSISTENSI DAN KESTABILAN SOLUSI GELOMBANG JALAN MODEL KUASILINER DISSIPATIF DUA KANAL

Pada paper ini akan dibahas solusi gelombang jalan model kuasilinear dissipatif dua kanal. Kecepatan gelombang ditentukan dengan syarat Rankine-Hugoniot. Solusi gelombang jalan heteroklinik dapat disajikan secara eksplisit dalam fungsi parameter. Dari penelitian diperoleh solusi gelombang jalan yang berupa gelombang kejut atau penyelesaian bernilai banyak (multivalued solution) yang mempunyai titik singular. Selanjutnya kestabilan solusi gelombang jalan dianalisa dengan metode energi. Keyword: solusi gelombang jalan, kestabilan, sistem hiperbolik tak linie

Transfer Function, Stabilizability, and Detectability of Non-autonomous Riesz-spectral Systems

Stability of a state linear system can be identified by controllability, observability, stabilizability, detectability, and transfer function. The approximate controllability and observability of non-autonomous Riesz-spectral systems have been established as well as non-autonomous Sturm-Liouville systems. As a continuation of the establishments, this paper concern on the analysis of the transfer function, stabilizability, and detectability of the non-autonomous Riesz-spectral systems. A strongly continuous quasi semigroup approach is implemented. The results show that the transfer function, stabilizability, and detectability can be established comprehensively in the non-autonomous Riesz-spectral systems. In particular, sufficient and necessary conditions for the stabilizability and detectability can be constructed. These results are parallel with infinite dimensional of autonomous systems

MODEL SIS DENGAN PERTUMBUHAN LOGISTIK

Dalam paper ini akan dibahas model interaksi satu spesies yang dipengaruhi oleh penyakit, dimana spesies tidak mengalami kekebalan setelah terinfeksi, sehingga kelas rentan berpindah ke kelas terinfeksi ketika terjadi penginfeksian dan akan kembali ke kelas rentan setelah penyembuhan (SIS). Lebih khusus model ini dibatasi dengan asumsi penyakit mengurangi reproduksi dan penyakit berelasi dengan kematian. Jika tidak ada penyakit, maka model merupakan persamaan logistik biasa, dengan pertumbuhan terbatas. Selanjutnya akan akan dianalisa kestabilan dan perilaku asimtotis di sekitar titik ekuilibriumnya. Kata kunci : Model SIS, Model pertumbuhan logisti

A Stability Mathematical Model of Nasopharyngeal Carcinoma on Cellular Level

This paper discussed the stability of “Tumorigenesis Models†to link between EBV and carcinoma of the nasopharyngeal from normal cell to invasive carcinoma. The review on this case accomplished the previous theorem of equilibrium point on “Tumorigenesis Modelsâ€

Link of Nasopharyngeal Carcinoma and Epstein-Barr Virus

Nasopharyngeal Carcinoma (NPC) is a cancer that occurs in nasopharynx which is associated with Epstein-Barr Virus (EBV). Mutation agents in nasopharyngeal neoplasms occur because of EBV infection. Transformation of B-cells due to EBV causes hormone imbalance in lymphoid cells or nasopharyngeal epithelial tissue. Rates of EBV infection have been shown to be prognostic to NPC. The basic level of EBV DNA can be used for stratification prognosis, with higher titers showing greater disease severity and worse outcomes. With mathematical models, there is a correlation between the increase in Epstein-Barr Virus and the increase in Invasive Carcinoma Cells or increase in Nasopharyngeal Carcinoma Cells

An age-structured SIPC model of cervical cancer with immunotherapy

Immunotherapy is a targeted therapy that can be applied to cervical cancer patients to prevent DNA damage caused by human papillomavirus (HPV). The HPV infects normal cervical cells withing a specific cell age interval, i.e., between the $G_1$ to $S$ phase of the cell cycle. In this study, we developed a new mathematical model of age-dependent immunotherapy for cervical cancer. The model is a four-dimensional first-order partial differential equation with time- and age-independent variables. The cell population is divided into four sub-populations, i.e., susceptible cells, cells infected by HPV, precancerous cells, and cancer cells. The immunotherapy term has been added to precancerous cells since these cells can experience regression if appointed by proper treatments. The immunotherapy process is closely related to the rate of T-cell division. The treatment works in the same cell cycle that stimulates and inhibits the immune system. In our model, immunotherapy is represented as a periodic function with a small amplitude. It is based on the fluctuating interaction between T-cells and precancerous cells. We have found that there are two types of steady-state conditions, i.e., infection-free and endemic. The local and global stability of an infection-free steady-state has been analyzed based on basic reproduction numbers. We have solved the Riccati differential equation to show the existence of an endemic steady-state. The stability analysis of the endemic steady-state has been determined by using the perturbation approach and solving integral equations. Some numerical simulations are also presented in this paper to illustrate the behavior of the solutions