THE GREATEST SOLUTION IN THE INEQUALITY OF K X X LX WITH K 2 ISnn;L 2 ISnn;X 2 ISnm ARE A COMPLETE IDEMPOTENT SEMIRINGS OF INTERVAL

The greatest solution of an inequality KX X LX to solve the optimalcontrol problem for P-Temporal Event Graphs, which is to nd the optimal control thatmeets the constraints on the output and constraints imposed on the adjusted model prob-lem (the model matching problem). We give the greatest solution K X X L Xand X H with K; L;X;H matrices whose are entries in a complete idempotent semir-ings. Furthermore, the authors examine the existence of a sucient condition of theprojector in the set of solutions of inequality K X X L X with K; L;X matrixwhose entries are in the complete idempotent semiring. Projectors can be very necessaryto synthesize controllers in manufacturing systems that are constrained by constraintsand some industrial applications. The researcher then examines the requirements forthe presence of the greatest solution was called projector in the set of solutions of theinequality K X X L X with K; L;X matrices whose are entries in an completeidempotent semiring of interval. Researchers describe in more detail the proof of theproperties used to resolve the inequality K X X L X. Before that, we givethe greatest solution of the inequality KX X LX and X G with K; L;X;Gmatrices whose are entries in an complete idempotent semiring of interval

PEMBUAT IDEAL MENDASAR (BASIC IDEALIZERS)

Diberikan ring S dan ideal kanan A. Dapat dibangun subring terbesar di S sedemikian sehingga A merupakan ideal dua sisi di subring tersebut. Struktur ini disebut pembuat ideal dan dinotasikan dengan R=I_S(A). Di dalam paper ini akan dibahas pembuat ideal dari ideal kanan isomaksimal generatif yang selanjutnya disebut pembuat ideal mendasar. Modul atas ring S dapat dipandang sebagai modul atas subring R. Modul atas ring S dapat dipandang sebagai modul atas subring R. Untuk sebarang subring R, beberapa sifat modulnya seperti sifat proyektif dan sifat sederhana tidak diawetkan ketika mengganti ring tumpuannya. Lebih lanjut, ditunjukkan bahwa jika R pembuat ideal mendasar, sifat-sifat ini diawetkan.Let S be a ring and A be a right ideal. We can construct the largest subring of S in which A be two sided ideal. This structure is called idealizer and denoted by R=I_S(A). In this paper we discuss idealizer of generative isomaximal right ideals that is called basic idealizer. Module over S can be viewed as modules over subring R. For arbitrary subrings R, some properties of modules such as projective dan simple are not preserved between when changing the ring. Furthermore, we show that under condition that R is basic idealizer, these properties are preserved.

Perinormalitas di Daerah Krull (Perinormality on Krull Domains)

Daerah integral R dikatakan perinormal jika untuk setiap overring (lokal) T dari R yang memenuhi kondisi going-down, maka T merupakan lokalisasi dari R pada ideal prima. Perinormalitas merupakan salah satu sifat ketertutupan integral. Dengan memperhatikan bahwa klosur integral dari daerah normal Noether merupakan daerah Krull, akan ditunjukkan bagaimana sifat perinormalitas di daerah Krull.An integral domain R is said to be perinormal if whenever T is a (local) overring of R such that the inclusion R in T satisfies going-down, it follows that T is a localization of R necessarily at a prime ideal. Perinormality is one of integral closedness property. As the integral closure of any Noetherian normal domain is Krull, it will be shown how perinormality behaves on Krull domains.

Subgrup Normal Multi-Fuzzy, Subgrup Normal Multi-Anti Fuzzy, Dan Teorema Korespondensi

In any group $ G $, we can form normal multi-fuzzy subgroups and normal multi-anti fuzzy subgroups. In this paper, we discuss the properties of normal multi-fuzzy subgroups and normal multi-anti fuzzy subgroups. Based on this structure, we construct the factor groups relative to a normal multi-fuzzy subgroup or normal multi-anti fuzzy subgroup. This gave rise to a one-to-one correspondence between the normal multi-anti fuzzy subgroups of a group $ G_2 $ and those of a group $ G_1 $ which are constant on the kernel of homomorphism $ f $. This correspondence can occur if $ f $ is epimorphism of groups from $ G_1 $ to $ G_2 $.

Max-Plus Linear Equation System and Its Application on Railway Network System

Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped with maximum operation and addition. Max-Plus algebra is able tomodel several types of Discrete Event System (DES) which are nonlinear in conventional algebra to be linear in Max-Plus algebra, so we can do further analysis of the system. Types of DES will be linear in the form of Max-Plus algebra which only synchronizes without any concurrency such as railway network systems, production systems, traffic lights, etc. This research discusses the application of the linear Max-Plus equation in the train schedules and involves synchronization between trains. The result of this study are obtained DAOP VI Yogyakarta rail network system model in the form of x(k + 1) = A otimes x (k) which is then used to determine the departure period and the time of initial train departure. The departure period is obtained from the eigenvalue (lambda) from the A matrix and the initial departure is obtained from the eigenvector corresponding to lambda. The calculation shows that the train departure period is T = 588 minutes.

Ring Konteks Morita dalam Suatu Ring Artin Sederhana

Diberikan ring R dan S, suatu (R,S)−bimodul V , dan suatu (S,R)−bimodul W. Misalkan T merupakan ring konteks Morita dengan komponen penyusunnya adalah R,V,W, dan S. Q(R) ring hasil bagi R, Q(S) ring hasil bagi S, Q(V ) modul hasil bagi V , dan Q(W) modul hasil bagi W. Dalam penelitian ini, ring T diasumsikan sebagai ring Goldie prima dengan ring hasil bagi dari T adalah Q(T) dengan komponen penyusunnya adalah Q(R),Q(V),Q(W), dan Q(S). Dengan kata lain, T merupakan order dalam suatu ring Artin sederhana Q(T). Lebih lanjut, akan diberikan beberapa syarat perlu dan cukup ring T merupakan order maksimal dan order Asano.

Sifat-Sifat Morfisma di dalam Kategori Ruang Penutup Ruang Topologis yang Terhubung Lintasan (On the Morphisms of the Category of Path Connected Covering Spaces )

Untuk sebarang ruang topologis $X$ dapat dibentuk $Cov_X$ yaitu kategori \linebreak ruang penutup $X$ yang terhubung lintasan. Pada tulisan ini akan dibahas syarat perlu dan cukup eksistensi morfisma antara dua ruang penutup yang terhubung lintasan lokal. Untuk sebarang $x_0 \in X$ dan grup fundamental $G=\pi_1(X,x_0)$, dapat dibentuk kategori $SetG$, yaitu kategori semua himpunan yang dilengkapi aksi kanan oleh $G$. Selanjutnya dibentuk fungtor $F$ dari $Cov_X$ ke $SetG$. Dalam tulisan dibuktikan bahwa $F$ bersifat \textit{fully faithful} jika $X$ terhubung lintasan dan terhubung lintasan lokal. Akibatnya untuk mengidentifikasi morfisma-morfisma antara dua obyek $A$ dan $B$ di $Cov_X$ dapat dilakukan dengan cara melihat sifat morfisma-morfisma antara $F(A)$ dan $F(B)$. (For any topological space $X$, we can construct the category of path \linebreak connected covering spaces of $X$, denoted by $Cov_X$. In this paper we study a sufficient and necesarry condition for the existence of morphism between two locally path \linebreak connected covering spaces. For every $x_0 \in X$ and fundamental group $G=\pi_1(X,x_0)$, we can construct the category of sets with right action of $G$, denoted by $SetG$. \linebreak Furthermore, we can define a functor $F$ from $Cov_X$ to $SetG$. We proof that the functor $F$ is fully faithul if $X$ is path connected and locally path connected. From this result, we can identify morphisms between $A$ and $B$ in $Cov_X$ by using the properties of morphisms between $F(A)$ and $F(B)$. )

MODEL GEOGRAPHICALLY WEIGHTED PANEL REGRESSION (GWPR) DENGAN FUNGSI KERNEL FIXED GAUSSIAN PADA INDEKS PEMBANGUNAN MANUSIA DI JAWA TIMUR

The Geographically Weighted Panel Regression (GWPR) model is a com-bination of panel data and GWR. The GWPR model is a development of the globalregression model where ideas are taken from non-parametric regression. This model is alinear regression model that is local (local linear regression) which produces an estima-tor of the model parameters that affects local for each point or location where the datais collected. The purpose of this study is form a GWPR model with a fixed gaussiankernel weighting function in overcoming the problem of spatial effects and geographicalfactors that affect an area to another region. The data used in this study is secondarydata taken from the Central Statistics Agency (BPS) website consisting of the HumanDevelopment Index in East Java 2013-2016. This study produces data for the making ofthe Human Development Index using the GWPR method in the formation of the model,where the coefficient of determination generated is 98,74%.Factors that increase HDI es-pecially Mojokerto Regency are average length of school (RLS), life expectancy (AHH),and the construction expensiveness index (IKK). Keywords: GWPR, Fixed Gaussian, Human Development Index, East Java.

ANALISIS KESTABILAN MODEL PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN LAJU INFEKSI TERSATURASI (STABILITY ANALYSIS OF TUBERCOLOSIS SPREAD DISEASES MODEL CONSIDERING SATURATED INFECTION RATE)

This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.

MODEL BERBASIS SIR DALAM PREDIKSI AWAL PENYEBARAN COVID-19 DI DAERAH ISTIMEWA YOGYAKARTA (DIY)

Pandemi COVID-19 yang muncul pertama kali pada akhir tahun 2019 saat ini telah menyebar ke seluruh dunia dan mempengaruhi segala sendi kehidupan manusia. Di Indonesia, kasus ini mulai berkembang sejak akhir bulan Februari 2020 dan hingga saat ini masih terus terjadi peningkatan infeksi baru. Beberapa model dan prediksi kasus COVID-19 di Indonesia telah dilakukan oleh para peneliti, namun hasilnya belum sepenuhnya akurat. Hal ini kemungkinan disebabkan adanya pola yang berbeda-beda di setiap daerah, sehingga prediksi yang dilakukan di tingkat nasional perlu mengakomodir perbedaan pola tersebut. Pada artikel ini, akan diperkenalkan model matematika untuk melakukan prediksi awal kasus COVID-19 di wilayah Daerah Istimewa Yogyakarta. Pemodelan dilakukan berbasis model SIR yang parameter-parameternya diestimasi berdasarkan data. Dengan menggunakan model tersebut, akan dikaji dua skenario yang bersifat optimistik dan pesimistik.