SISTEM PENDUKUNG KEPUTUSAN PENERIMAAN BEASISWA BIDIKMISI DI UINSA DENGAN MENGGUNAKAN ANALYTICAL HIERARCHY PROCESS (AHP)

<p class="AfiliasiCxSpFirst" align="left"><strong>Abstrak:</strong></p><p class="AfiliasiCxSpMiddle"> Beasiswa merupakan pemberian bantuan biaya pendidikan kepada mahasiswa yang mampu dalam bidang akademik tetapi tidak dalam perekonomian. Namun masih sering terjadi kendala dalam pemrosesan seleksi pendaftar beasiswa, yaitu banyaknya kriteria yang harus diperhatikan dan banyaknya data pendaftar sehingga pengambilan keputusan menjadi relatif lebih sulit. Tujuan dari penelitian ini adalah memberikan alternatif dalam pengambilan keputusan penerima bantuan beasiswa untuk mahasiswa fakultas sains dan teknologi UINSA dengan menggunakan metode <em>Analytical Hierarchy Process (</em>AHP). Data yang diolah adalah data primer yang diperoleh dari angket. Data yang telah terkumpul selanjutnya dianalisis dengan matriks perbandingan berpasangan untuk menentukan nilai eigen dan vektor eigen. Hasil penelitian menunjukkan bahwa dari 39 pendaftar diperoleh 12 pendaftar yang menjadi prioritas dalam mendapatkan beasiswa Bidikmisi. Berturut-turut mahasiswa dengan kode Z1, Z2, Z5, Z7, Z10, Z19, Z20, Z21, Z23, Z29, Z32, Z35 dengan masing-masing bobot sebesar 0.34%, 0.27%, 0.27%, 0.28%, 0.36%, 0.33%, 0.29%, 0.31%, 0.34%, 0.29%, 0.27%, 0.35%.</p><p class="AfiliasiCxSpMiddle" align="left"> </p><p class="AfiliasiCxSpLast" align="left"><strong>Kata Kunci</strong>:</p><p>Vektor<em> </em>Eigen<em>, Analytical Hierarchy Process </em>(AHP)<em>, </em>Nilai<em> </em>Eigen</p><p> </p><p class="AfiliasiCxSpFirst" align="left"><strong><em>Abstract:</em></strong></p><p class="AfiliasiCxSpMiddle"><em>The scholarship is the provision of tuition assistance to students who are capable of academics but have difficulties economically. However, some obstacles are often found throughout the screening process of scholarship applicants, such as the number of criteria to fulfill and the number of registrant data that results in difficulties in making a decision</em><em>. </em><em>This study aims to provide an alternative in decision making on the screening process of scholarship applicants for students from the Faculty of Science and Technology at the Universitas Islam Negeri Sunan Ampel by using the Analytical Hierarchy Process (AHP)</em><em>. </em><em>The data processed are from the primary data obtained from questionnaires. The data obtained were analyzed by using a pairwise comparison matrix to determine the eigenvalues and eigenvectors. The results indicate that of 39 registrants, 12 of them became a priority in getting the Bidikmisi scholarship</em><em>. </em><em>Consecutively, students with codes</em><em> Z1, Z2, Z5, Z7, Z10, Z19, Z20, Z21, Z23, Z29, Z32, Z35 </em><em>have the score of</em><em> 0.34%, 0.27%, 0.27%, 0.28%, 0.36%, 0.33%, 0.29%, 0.31%, 0.34%, 0.29%, 0.27%, 0.35%.</em><em></em></p><p class="AfiliasiCxSpMiddle" align="left"><strong><em> </em></strong></p><p class="AfiliasiCxSpLast" align="left"><strong><em>Keywords</em></strong><em>:</em></p><em>Eigenvector, Analytical Hierarchy Process</em> (AHP), <em>Eigenvalue</em>

Dirac oscillator in dynamical noncommutative space

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by a dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in the dynamical noncommutative space, in which the space-space Heisenberg-like commutation relations and noncommutative parameter are position-dependent. Then, we used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the language of creation and annihilation operators and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that, with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS

Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph. The communication graph can be strongly connected graph and a not strongly connected graph. The representation matrix of a strongly connected graph is called an irreducible matrix, while the representation matrix of a graph that is not strongly connected is called a reduced matrix. The purpose of this research is set the steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and also eigenmode of the regular reduced matrix over min-plus algebra. Min-plus algebra has an ispmorphic structure with max-plus algebra. Therefore, eigen problems and eigenmode matrices over min-plus algebra can be determined based on the theory of eigenvalues, eigenvectors and eigenmode matrices over max-plus algebra. The results of this research obtained steps to determine the eigenvalues and eigenvectors of the irreducible matrix over min-plus algebra and eigenmode algorithm of the regular reduced matrix over min-plus algebra

Sensitivity Analysis Using a Reduced Finite Element Model for Structural Damage Identification

Sensitivity analysis is widely used in engineering fields, such as structural damage identification, model correction, and vibration control. In general, the existing sensitivity calculation formulas are derived from th,,,e complete finite element model, which requires a large amount of calculation for large-scale structures. In view of this, a fast sensitivity analysis algorithm based on the reduced finite element model is proposed in this paper. The basic idea of the proposed sensitivity analysis algorithm is to use a model reduction technique to avoid the complex calculation required in solving eigenvalues and eigenvectors by the complete model. Compared with the existing sensitivity calculation formulas, the proposed approach may increase efficiency, with a small loss of accuracy of sensitivity analysis. Using the fast sensitivity analysis, the linear equations for structural damage identification can be established to solve the desired elemental damage parameters. Moreover, a feedback-generalized inverse algorithm is proposed in this work in order to improve the calculation accuracy of damage identification. The core principle of this feedback operation is to reduce the number of unknowns, step by step, according to the generalized inverse solution. Numerical and experimental examples show that the fast sensitivity analysis based on the reduced model can obtain almost the same results as those obtained by the complete model for low eigenvalues and eigenvectors. The feedback-generalized inverse algorithm can effectively overcome the ill-posed problem of the linear equations and obtain accurate results of damage identification under data noise interference. The proposed method may be a very promising tool for sensitivity analysis and damage identification based on the reduced finite element model.

Two Chebyshev Spectral Methods for Solving Normal Modes in Atmospheric Acoustics

The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a time-independent single-frequency sound source. Its solution consists of a set of discrete modes radiating into the upper atmosphere, usually related to the continuous spectrum. In this article, we present two spectral methods, the Chebyshev-Tau and Chebyshev-Collocation methods, to solve for the atmospheric acoustic normal modes, and corresponding programs are developed. The two spectral methods successfully transform the problem of searching for the modal wavenumbers in the complex plane into a simple dense matrix eigenvalue problem by projecting the governing equation onto a set of orthogonal bases, which can be easily solved through linear algebra methods. After the eigenvalues and eigenvectors are obtained, the horizontal wavenumbers and their corresponding modes can be obtained with simple processing. Numerical experiments were examined for both downwind and upwind conditions to verify the effectiveness of the methods. The running time data indicated that both spectral methods proposed in this article are faster than the Legendre-Galerkin spectral method proposed previously.