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All Journal Jurnal INKOM Journal of the Indonesian Mathematical Society Journal of Mathematical and Fundamental Sciences Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Hendra Gunawan
Institut Teknologi Bandung
Astronomy Chemistry Computer Science & IT Earth & Planetary Sciences Mathematics Physics

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Peningkatan Kinerja Skema Estimasi Arah Kedatangan Sinyal dengan Compressive Sensing Sparsitas Sudut dan Sampel Multisnap Koredianto Usman; Andriyan Bayu Suksmono; Hendra Gunawan
INKOM Journal Vol 8, No 1 (2014)
Publisher : Pusat Penelitian Informatika - LIPI

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14203/j.inkom.380

Abstract

Perkembangan teknik compressive sensing beserta pemanfaatannya digunakan pada berbagai penyelesaian permasalahan. Salah satu pemanfaatannya yang dibahas di sini adalah untuk pengurangan sampel pada skema estimasi arah kedatangan sinyal. Secara umum terdapat tiga skema besar pemanfaatan teknik compressive sensing untuk estimasi arah kedatangan: skema sparsitas frekuensi, skema sparsitas spasial dan skema sparsitas sudut. Dari ketiga teknik ini, skema sparsitas sudut menjadi fokus pada penelitian ini karena keuntungannya dalam mengurangi sampel yang superior dibandingkan dengan dua skema lainnya. Keuntungan lain dari skema ini adalah kesederhanaannya. Kekurangan dari skema ini adalah sensitifitas terhadap noise. Pada lingkungan dengan noise tinggi dengan SNR kurang dari 0 dB, skema ini menderita kesalahan estimasi sudut di atas lima derajat. Tingkat kesalahan estimasi meningkat pada level yang tidak dapat lagi diterima untuk SNR kurang dari -5 dB. Peningkatan ketahanan terhadap noise yang dilakukan pada penelitian ini adalah dengan menggunakan teknik multisnap sampel. Ada dua skema yang diusulkan yaitu teknik multisnap sederhana dan teknik multisnap dengan outliers removal. Hasil simulasi menunjukkan teknik multisnap sederhana meningkatkan akurasi sekitar 2 derajat pada SNR 0 dB. Pada SNR -5 dB terjadi peningkatan akurasi secara signifikan di atas 10 derajat. Pada teknik multisnap dengan outliers removal terjadi peningkatan akurasi lebih lanjut pada SNR kurang dari -5 dB.
EQUIVALENCE OF n-NORMS ON THE SPACE OF p-SUMMABLE SEQUENCES Anwar Mutaqin; Hendra Gunawan
Journal of the Indonesian Mathematical Society Volume 16 Number 1 (April 2010)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.16.1.27.1-7

Abstract

We study the relation between two known n-norms on lp, the space ofp-summable sequences. One n-norm is derived from GÄahler's formula (1969), whilethe other is due to Gunawan (2001). We show in particular that the convergence inone n-norm implies that in the other. The key is to show that the convergence ineach of these n-norms is equivalent to that in the usual norm on lp.DOI : http://dx.doi.org/10.22342/jims.16.1.27.1-7
ON b-ORTHOGONALITY IN 2-NORMED SPACES S. M. Gozali; Hendra Gunawan
Journal of the Indonesian Mathematical Society Volume 16 Number 2 (October 2010)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.16.2.36.127-132

Abstract

In this note we discuss the concept of b-orthogonality in 2-normedspaces. We observe in particular that this denition of orthogonality is too loose sothat every two linearly independent vectors are b-orthogonal.DOI : http://dx.doi.org/10.22342/jims.16.2.36.127-132
Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes Nicky Tumalun; Hendra Gunawan
Journal of the Indonesian Mathematical Society Volume 25 Number 3 (November 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.3.817.203-209

Abstract

In this paper, we show that the Morrey spaces $ L^{1,\left( \frac{\lambda}{p} -\frac{n}{p} + n \right) } \left( \mathbb{R}^{n} \right) $ are embedded betweenweak Morrey spaces $ wL^{p,\lambda}\left( \mathbb{R}^{n} \right) $ and Stummelclasses $ S_{\alpha}\left( \mathbb{R}^{n} \right) $ under some conditions on$ p, \lambda $ and $ \alpha $. More precisely, we prove that $ wL^{p,\lambda}\left(\mathbb{R}^{n} \right) \subseteq L^{1,\left( \frac{\lambda}{p} - \frac{n}{p} + n\right) } \left( \mathbb{R}^{n} \right) \subseteq S_{\alpha}\left( \mathbb{R}^{n}\right) $ where $ 1<p<\infty, 0<\lambda<n $ and $ \frac{n-\lambda}{p}<\alpha<n $.We also show that these inclusion relations under the above conditions are proper.Lastly, we present an inequality of Adams' type \cite{A}
On Birkhoff Angles in Normed Spaces Hendra Gunawan; Muhamad Jamaludin; Mas Daffa Pratamadirdja
Journal of the Indonesian Mathematical Society VOLUME 27 NUMBER 3 (November 2021)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.27.3.1030.270-284

Abstract

Associated to Birkhoff orthogonality, we study Birkhoff angles in a normed space and present some of their basic properties. We also discuss how to decide whether an angle is more acute or more obtuse than another. In addition, given two vectors $x$ and $y$ in a normed space, we study the formula for Birkhoff `cosine' of the angle from $x$ to $y$ from which we can, in principal, compute the angle. Some examples will be presented.
Inclusion Properties of Orlicz and Weak Orlicz Spaces Al Azhary Masta; Hendra Gunawan; Wono Setya Budhi
Journal of Mathematical and Fundamental Sciences Vol. 48 No. 3 (2016)
Publisher : Institute for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2016.48.3.1

Abstract

This paper discusses the structure of Orlicz spaces and weak Orliczspaces on ℝn. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the characteristic functions of the balls in ℝn.
KETAKSAMAAN HERMITE-HADAMARD TERHADAP INTEGRAL RIEMANN-STIELTJES Denny Ivanal Hakim; Hendra Gunawan
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 4 No 1 (2012): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2012.4.1.2942

Abstract

The Hermite-Hadamard inequality is an inequality for convex functions that gives an estimate for the integral mean value of a convex function on a closed interval by its value at the middle of interval and the average of its values at the endpoints. The Hermite-Hadamard inequality can be generalized by using the Riemann-Stieltjes integral mean value. An application of the Hermite-Hadamard inequality with respect to Riemann-Stieltjes integral for estimating the power mean of positive real numbers by the aritmethic mean is given at the end of discussion.
Co-Authors Andriyan Bayu Suksmono, Andriyan Bayu Andriyan Suksmono Anwar Mutaqin Denny Ivanal Hakim Koredianto Usman Kusworo Adi Mas Daffa Pratamadirdja Masta, Al Azhary Muhamad Jamaludin Nicky Kurnia Tumalun S. M. Gozali Tati Mengko Wono Setya Budhi