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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika Teknik Sipil dan Arsitektur JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI CAUCHY: Jurnal Matematika Murni dan Aplikasi Resital: Jurnal Seni Pertunjukan (Journal of Performing Arts) Journal of Degraded and Mining Lands Management Journal of Natural Sciences and Mathematics Research Al-Jabar : Jurnal Pendidikan Matematika Asia-Pacific Management and Business Application JURNAL ILMIAH MATEMATIKA DAN TERAPAN JMPM: Jurnal Matematika dan Pendidikan Matematika Adi Widya : Jurnal Pengabdian Masyarakat BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Labora Medika JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya Jambura Journal of Mathematics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jurnal Matematika UNAND Mandalika Mathematics and Educations Journal Jurnal Borneo Akcaya : Jurnal Penelitian dan Pengembangan Pelayanan Publik Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Leibniz: Jurnal Matematika Journal of Mathematics: Theory and Applications Empowerment Society Muria Jurnal Layanan Masyarakat Asia Pacific Journal of Management and Education Jurnal Matematika Integratif Mathematical Sciences and Applications Journal Indonesian Journal of Applied Mathematics and Statistics
Edi Kurniadi
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Lattices Constructions for Euclidean Space Rn and its Subspaces Hayyah, Zahira Najmatul; Kurniadi, Edi; Triska, Anita
Jambura Journal of Mathematics Vol 8, No 1: February 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i1.36272

Abstract

A lattice is a discrete subgroup of n-dimensional Euclidean space that serves as a fundamental object of study in Algebra and the Geometry of Numbers. This structure has significant applications in various fields, particularly in lattice-based cryptography and coding theory. This paper aims to present the formal construction of lattices for $n$-dimensional Euclidean space Rn and its linear subspaces by analyzing the formal definitions and essential properties of lattices. The main results of this research lie in two main results which are presented in several propositions. First, the set Zn of standard integer points is proven to be a lattice in n-dimensional space with respect to the standard basis of V \subseteq Rn. Second, the set of integer points whose last component is zero is proven to be a lattice within (n-1)-dimensional non-trivial subspaces. Indeed, in this case, the obtained lattice is not equal to Zn. Moreover, it also discussed the lattices of a non-standard basis for V. Explicitly, this work contributes a rigorous formal verification that integer structures within subspaces, such as Z{n-1}x0, retain fundamental lattice properties even under non-standard basis constructions.
On the Structural Relationship Between the Characteristic and Minimal Polynomials of a Linear Operator Suharto, Istiqomah; Kurniadi, Edi; Carnia, Ema
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.68420.37-58

Abstract

In this paper, we study the relationship between the characteristic and minimal polynomial of a linear operator, with a focus on figuring out under what conditions that the two polynomials equal each other. We emphasize that the characteristic and minimal polynomial of a linear operator are the same if and only if every eigenvalue has a geometric multiplicity of 1, which is equivalent to having only one Jordan block per eigenvalue. We provide an alternative proof for such a theory. For such matrices, we also show that the minimal polynomial can be easily derived from the normalized linear dependence of the Krylov sequence $\{v, Av, A^2v, \dots, A^{n-1}v\}$ for any generic vector $v$. We apply these algorithms to analyze the nilpotent and companion matrices. The results algorithmically verify that for a companion matrix $C$, its characteristic and minimal polynomials are identical and equal to its generating polynomial, $p_C(X)=m_C(X)=f(X)$. For a nilpotent matrix $N$ with index $k$, we confirm that its minimal polynomial is $m_N(X)=X^k$.
KUAT LENTUR MORTAR BERSERAT DENGAN MEMANFAATKAN LIMBAH BATA MERAH SEBAGAI SUBSTITUSI SEMEN Kurniadi, Edi; Kurniawan, Agus; Himawan, Lava; Pratiwi, Nursifa Maulidini Rahma
Jurnal Teknik Sipil dan Arsitektur Vol 31 No 2 (2026): Jurnal Teknik Sipil dan Arsitektur
Publisher : Fakultas Teknik Universitas Tunas Pembangunan Surakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36728/jtsa.v31i2.6216

Abstract

The increase in infrastructure development activity in Indonesia has directly impacted the rising demand for construction materials, including red bricks. The red brick production process generates significant residue, where a single firing cycle can result in approximately 300 pieces of waste bricks, equivalent to 1.2% of total production. To provide an environmentally friendly solution, red brick waste is utilized as a partial substitute for cement in mortar production, along with the addition of roving fibers to enhance flexural strength performance. This study aims to examine the utilization of red brick waste as a cement substitute in mortar combined with the addition of roving fibers and its effect on flexural strength. The research employed a quantitative experimental method at the Building Materials Laboratory, Department of Civil Engineering, Vocational School, Universitas Gadjah Mada. The study utilized cement-to-sand mix ratios of 1:2, 1:3, 1:4, 1:5, and 1:6, with Portland cement substitution variations using red brick powder at 0%, 2.5%, 5%, 7.5%, and 10%. Roving fibers, cut to a length of 1 cm, were added at 2% by weight of cement. The specimens consisted of mortar beams with dimensions of 40x40x160 mm, tested at 28 days of age. The results indicated that for non-fiber mortar, the highest flexural strength was achieved at a 1:2 ratio with 0% substitution, reaching 4.62 MPa. The maximum flexural strength was recorded at a 1:2 ratio with 2.5% red brick waste substitution and 2% roving fibers, measuring 5.13 MPa. Significantly, the addition of roving fibers improved mortar performance. A 20.7% increase in flexural strength was observed at the 1:2 ratio with 2% roving fibers and 2.5% cement substitution when compared to the mortar with 2.5% cement substitution without fibers, demonstrating the effectiveness of red brick waste and roving fibers as sustainable alternative materials.
Co-Authors Agus Kurniawan Alamsyah, Alifa Raida Alit Kartiwa Aminuyati Anita Triska Ari Hepi Yanti Arifah, Siti Asri Laksmi Riani Asri Laksmi Riani Atmaji, Susan Dwi Cahyaningrum Aurillya Queency Badrulfalah Badrulfalah Betty Subartini Cholil, Mohammad Dellavani, Charitra Yulia Dien Wardihastri Destina Paningrum, Destina Diah Wulandari Rousdy Dwi Soegiarto, Dwi Ema Carnia Estetika Mutiaranisa Kurniawati Faza, Novan Ramadhani Nur Firdaniza Firdaniza Hafizhah, Nur Hasan, Nabila Nurmala Hayyah, Zahira Najmatul Henti, Henti Hermawan, Aldi Himawan, Lava Hisjam, Muhammad Holyness Nurdin Singadimedja Ida Ayu Suci Irawati Irawati Isah Aisah Kankan Parmikanti Khairudin Khairudin Kurniawati, Estetika Mutiaranisa Maharani, Saskia Putri Masulili, Agusalim Mohammad Cholil Muhammad Arief Budiman Mulyanto Mulyanto Nurul Gusriani Pratiwi, Nursifa Maulidini Rahma Pratiwi, Putri Nisa Putra, Ricardo Eka Queency, Aurillya Rahmawati, Rahmawati Rikah, Rikah Rikhsan Kurniatuhadi, Rikhsan Rini Suryani, Rini Rudianto Rudianto Rudianto, M Rusnandari Retno Cahyani Sarah Rum Handayani Sarwono Sarwono Setiawan, Ade Ripki Sisilia Sylviani Siti Nurlaela siti nurlela Slamet Supriyadi Slamet Supriyadi Sri Murni SRI RAHAYU Stanley P. Dewanto, Stanley P. Suci, Ida Ayu Suharto, Istiqomah Sukono Sukono Sumartono, Basuki Susan Dwi Cahyaningrum, Atmaji, Sutikarini Tielung, M. Fariel Fahriza Wahida , Adam