wakil ketua - kamindo · 2019. 9. 6. · sanata dharma university email: [email protected]....

$: WAKIL KETUA - KAMINDO · 2019. 9. 6. · Sanata Dharma University Email: herrypribs@usd.ac.id. ABSTRAK. In this paper we study the sub-fractional Brownian motion in the framework$

Ratno Bagus Edy Wibowo, S.Si, M.Si, Ph.D

Jalina Widjaja, Ph.D

1. Prof. Hendra Gunawan, Ph.D.

2. Prof. Dr. Supama, M.Si.

3. Prof. Dr. Marjono, M.Phil.

4. Prof. Dr. Mashadi, M.Si.

5. Prof. Wono Setya Budhi, Ph.D.

6. Prof. Dr. Ch. Rini Indrati, M.Si.

7. Yudi Soeharyadi, Ph.D.

KETUA

WAKIL KETUA

Dr. Nanang Susyanto, S.Si, M.Sc

BENDAHARA

Rektor Universitas Pelita Harapan

PELINDUNG

Kie Ivanky Saputra, Ph.D

KETUA PANITIA

Lina Tjahjadi

Helena Margaretha

Calvin Gunawan

Beta Zionetha Mailoa

Inggrid Meyliana Tirta

WAKIL KETUA

ACARA

Ferry V Ferdinand

Michael Wibowo

Reynaldi

Tenny Mariana

Karunia Pormes

PROSIDING

ORGANIZING COMMITTEE

SCIENTIFIC BOARD

Sumatera & Kalimantan :

Dr. Pardomuan Sitompul, S.Si, M.Si

Dr. Sri Gemawati, M.Si

Jawa Barat, Banten, DKI :


Jawa Tengah & DIY :

Dr. Herry Pribawanto Suryawan

Jawa Timur, Bali, NTT, NTB :

Dr. Eridani, M.Si

Sulawesi, Maluku, & Papua :

Prof. Dr. Eng. H. Mawardi Bahri, M.Si

PENGURUS WILAYAH

KAMINDO

Kata Pengantar

Simposium Nasional Analisis Matematika dan Aplikasinya (SNAMA 2019) yang diselenggarakan diUniversitas Pelita Harapan, Karawaci pada tanggal 6-7 September 2019 ini merupakan salah satuprogram untuk mewujudkan visi dan misi KAMINDO dalam mengembangkan matematika analisisdan pengajarannya di Indonesia secara berkelanjutan. Selain itu, kegiatan SNAMA 2019 merupakanbentuk kolaborasi penyelenggaraan seminar nasional antara KAMINDO dan Universitas PelitaHarapan yang bertujuan untuk menjadi ajang diskusi, pemutakhiran wawasan pada bidang analisismatematika, dan kolaborasi antar peminat dan pengguna analisis matematika. Selanjutnya,diharapkan dengan adanya kegiatan ini dapat meningkatkan kualitas pembelajaran analisismatematika melalui workshop pembelajaran yang membahas berbagai topik dalam bidang analisis.

KAMINDO menyampaikan terimakasih dan penghargaan yang setinggi-tingginya kepada PanitaPenyelenggara, khususnya Fakultas Sains dan Teknologi Universitas Pelita Harapan atas terjalinnyakerjasama baik dalam penyelenggaran simposium ini. Tidak lupa pula, kami ucapkan terimakasihkepada Scientific Board KAMINDO yang telah banyak memberikan masukan sehingga SNAMA 2019ini berjalan dengan lancar.

Besar harapan kami, kerjasama yang baik ini juga dapat meluas dan terintegrasi di seluruh wilayahIndonesia.

Ketua KAMINDO,

Ratno Bagus Edy Wibowo, S.Si, M.Si, Ph.D

Kata Pengantar

Program Studi Matematika, Fakultas Sains dan Teknologi, Universitas Pelita Harapan pada tahun2019 ini, mendapat kehormatan dari Komunitas Analisis Matematika Indonesia (KAMINDO) untukmenjadi tuan rumah Simposium Nasional Analisis Matematika dan Aplikasinya (SNAMA).Simposium ini, yang merupakan acara tahunan dari KAMINDO, telah diadakan untuk yang keduabelas kalinya, bekerja sama dengan universitas-universitas di seluruh Indonesia.

Dalam SNAMA 2019, terdapat dua kegiatan utama yakni workshop pembelajaran MatematikaAnalisis dengan topik limit fungsi dan barisan fungsi yang dilaksanakan pada hari Jumat, 06September 2019. Kegiatan kedua adalah simposium yang akan dilaksanakan pada hari Sabtu, 07September 2019. Di dalam dua kegiatan tersebut, SNAMA 2019 dapat menjadi tempat belajar bagipara peminat dan pengguna di bidang Matematika Analisis dan juga tempat berdiskusi bagi penelitiMatematika Analisis di Indonesia. Hal ini sangatlah sesuai dengan visi dan misi Program StudiMatematika yang bertujuan untuk mengembangkan matematika dan aplikasi matematika sampai keseluruh Indonesia dan juga mengembangkan kerjasama dan penelitian dengan universitas-universitas lain di seluruh Indonesia.

Program Studi Matematika juga ingin mengucapkan terima kasih sebesar-besarnya kepadapengurus KAMINDO yang telah mempercayakan SNAMA 2019 kepada kami, tak lupa kami jugamengucapkan terima kasih kepada Scientific Board dari KAMINDO yang telah memberikandukungan dan masukan agar acara ini dapat berjalan dengan lancar. Akhir kata, kami jugabersyukur kepada Tuhan yang Maha Esa agar acara ini juga dapat bermanfaat bagi seluruhkomunitas yang ada.

Selamat menikmati simposium ini !

Ketua Panitia SNAMA 2019,


Auto-generated: 6-09-2019 iii/iv

Daftar Isi

PEMBICARA UTAMA 1 .......................................................................................................

1 Some Results Related to Two-Dimensional Quaternion Linear Canonical Transform 3 ............................

2 Dynamical Systems Analysis of Local and Non-Local Dispersal Models 4 .............................................

PEMBICARA UTAMA 1 .......................................................................................................

1 Weighted Local Times of Sub-fractional Brownian Motion as White Noise Distributions 3 .......................

2 Some Fixed Point Theorems in Ultrametric Spaces 4 ..........................................................................

3 $n$-Normed Spaces with Respect To Norms of Its Quotient Spaces 5 .................................................

4 Sufficient and Necessary Conditions for Holder’s Inequality in Weighted Orlicz Spaces 6 .......................

5 Operator Integral Fraksional dengan Rough Kernel di Ruang Morrey diperumum-$\theta$ 7 ...................

6 Embeddings of Discrete Morrey Spaces 8 ..........................................................................................

7 Littlewood-Paley Theory on Morrey Space 9 ........................................................................................

8 Initial Coefficients for Bazilevic Functions in a Sector 10 .....................................................................

9 On Bounded Topological B-Algebra 11 ...............................................................................................

10 Dynamical Systems Analysis of Local and Non-Local Dispersal Models 12 .........................................

11 Teorema Titik Tetap untuk Turunan dari Fungsi Bernilai Interval 13 ....................................................

12 Perhitungan Kesalahan Deret Cosinus dengan Koefisien dari Klas Monoton Umum Orde $r$ 14 ..........

13 A Case of Differential Equation with Single Stochastic Time Delay 15 ................................................

14 Eksistensi Solusi Lemah untuk Masalah Cauchy-Dirichlet pada Sistem p-Laplacian 16 ........................

15 Fefferman\'s Inequality and Unique Continuation Property of Elliptic Partial Differential Equations17 ...............................................................................................................................................

16 Iterative Operator Splitting Method for A Class of Fisher\'s Equation 18 ............................................

17 Aproksimasi Fungsi di $L^p$ dengan Konvolusi 19 ..........................................................................

SNAMA 2019

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SNAMA 2019

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K E Y N O T E S P E A K E R

PEMBICARA UTAMA

SNAMA 2019

2/6

SNAMA 2019 / KEYNOTE SPEAKER ANALISIS KOMPLEKS


Some Results Related to Two-Dimensional QuaternionLinear Canonical Transform

MAWARDI BAHRI

Department of Mathematics, Hasanuddin University, Makassar 90245, Indonesia

Email: [email protected]

ABSTRAK

We introduce a definition of the two-dimensional quaternion linear canonical transform (QLCT). The

transform is constructed by replacing the Fourier transform kernel with the quaternion Fourier

transform (QFT) kernel in the definition of the classical linear canonical transform(LCT). Applying

QlCT kernel we establish several properties of the QLCT. Based on the convolutions and

correlations definition of the LCT and QFT, convolution and correlation theorems associated with the

QLCT are studied. An uncertainty principle for the QLCT is established. It is shown that the

localization of a quaternion-valued function and the localization of the QLCT are inversely

proportional and that only modulated and shifted two-dimensional Gaussian functions minimize the

uncertainty.

KATA KUNCI : linear canonical transform, convolution, correlation

SNAMA 2019 / 10 / ID36 ANALISIS KOMPLEKS

4/6

Dynamical Systems Analysis of Local and Non-LocalDispersal Models

DR. MOHD HAFIZ MOHD

School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia


ABSTRAK

In this talk, we discuss the effects of different dispersal patterns on the occurrence of priority

effects (alternative stable states) and coexistence in multi-species communities by employing local

(partial-differential equations) and non-local dispersal (integro-differential equations) models. Our

analysis shows the existence of a threshold value in dispersal strength (i.e. saddle-node

bifurcation) above which priority effects disappear. These results also reveal a co-dimension 2

point, corresponding to a degenerate transcritical bifurcation: at this point, the transcritical

bifurcation changes from subcritical to supercritical with corresponding creation of a saddle-node

bifurcation curve.

KATA KUNCI : dispersal patterns, partial-differential equations, integro-differential equations

0


SNAMA 2019

6/6


P E M A K A L A H

SNAMA 2019

SNAMA 2019

2/21

0


Weighted Local Times of Sub-fractional BrownianMotion as White Noise Distributions

HERRY PRIBAWANTO SURYAWAN

Sanata Dharma University


ABSTRAK

In this paper we study the sub-fractional Brownian motion in the framework of white noise analysis.

In particular we show that Donsker‘s delta functionals of a sub-fractional Brownian motion is an

element of the space of Hida distributions. Using this result we prove the existence of the weighted

local times of a -dimensional sub-fractional Brownian motion as white noise distributions.

KATA KUNCI : weighted local times, sub-fractional Brownian motion, white noise analysis

SNAMA 2019 / 2 / ID22 ANALISIS FUNGSIONAL

4/21

Some Fixed Point Theorems in Ultrametric Spaces

MICHAEL INUHAN1, CH.RINI INDRATI2

1, 2Universitas Gajah Mada

Email: [email protected], [email protected]

ABSTRAK

In this paper it will be discussed some fixed point theorems in ultrametric spaces. By using

spherically complete properties, it can be shown that there exists a unique fixed point of a strictly

contractive function. Furthermore, it will be shown there exists a fixed point of strictly contracting

on orbits function as a generalization concept of strictly contractive function. At the end of this

paper, it will shown the existence of a fixed point which becomes the nearest point of an element in

ultrametric space.

KATA KUNCI : ultrametric space, spherically complete, strictly contraction, fixed point

0


-Normed Spaces with Respect To Norms of ItsQuotient Spaces

HARMANUS BATKUNDE1, HENDRA GUNAWAN2

1, 2Institut Teknologi Bandung


ABSTRAK

In this paper, we investigate some features of the -normed spaces. We use norms of its quotient

spaces to study convergence sequences, closed sets, and bounded sets in the -normed spaces.

These norms will be a new viewpoint in observing the characteristics of the -normed spaces.

Moreover, instead of using all norms of the quotient spaces to examine these features, we show

that we can use only some norms of the quotient spaces. We also show the least number of norms

of the quotient spaces that we can choose to review these features of the -normed spaces.

KATA KUNCI : bounded sets, closed sets, -normed spaces

SNAMA 2019 / 4 / ID29 ANALISIS FUNGSIONAL

6/21

Sufficient and Necessary Conditions for Holder’sInequality in Weighted Orlicz Spaces

IFRONIKA1, AL AZHARI MASTA2, SITI FATIMAH3

1Institut Teknologi Bandung2, 3Universitas Pendidikan Indonesia

Email: [email protected], [email protected], [email protected]

ABSTRAK

In this talk, we discuss the sufficient and necessary conditions for generalized Holder’s inequality in

weighted Orlicz spaces and in their weak type. One of the keys to prove our results is to estimate

the norms of characteristic function in R^n.

KATA KUNCI : Holder’s inequality, Orlicz spaces, weighted Orlicz spaces

0


Operator Integral Fraksional dengan Rough Kernel diRuang Morrey diperumum-

DANIEL SALIM1, WONO SETYA BUDHI2, YUDI SOEHARYADI3

1, 2, 3Insititut Teknologi Bandung


ABSTRAK

Pada setengah abad terakhir, kajian keterbatasan operator integral di ruang Morrey berkembang

pesat. Ruang Morrey sendiri memiliki dua tipe variasi perumuman, seperti ruang Morrey diperumum-

yang diperkenalkan oleh Nakai, dan ruang Morrey diperumum- yang pertama kali dikaji oleh

Adams. Pada tahun 2017, Salim dkk telah membuktikan sifat keterbatasan operator integral

fraksional dengan rough kernel di ruang Morrey diperumum- . Pada kesempatan ini, keterbatasan

operator integral dengan rough kernel dikaji di ruang Morrey diperumum- .

KATA KUNCI : Ruang Morrey diperumum- , Operator integral fraksional dengan rough kernel,ketaksamaan Adams, ketaksamaan Spanne.

SNAMA 2019 / 6 / ID26 ANALISIS HARMONIK

8/21

Embeddings of Discrete Morrey Spaces

HENDRA GUNAWAN1, DENNY IVANAL HAKIM2, MOCHAMMAD IDRIS3

1, 2Kelompok Keahlian Analisis dan Geometri institut Teknologi Bandung3Departemen Matematika Universitas Lambung Mangkurat


ABSTRAK

In this talk, we discuss several embeddings between discrete Morrey spaces. We give a necessary

condition for these embeddings. We also discuss some connections between embeddings of

discrete Morrey spaces and those of Morrey spaces.

KATA KUNCI : Discrete Morrey spaces, Embeddings, Morrey spaces.

0


Littlewood-Paley Theory on Morrey Space

PEBRUDAL ZANU1, YUDI SOEHARYADI2, WONO SETYA BUDHI3

1, 2, 3Institut Teknologi Bandung


ABSTRAK

Fourier series can considered as a way to decompose a periodic function on . Littlewood-Paley

pushed the idea further to decompose non periodic function on and functions on for .

The decomposition is applied to a Fourier transform of a given function, using a multiplier in

frequency domain. A sequence is produced upon this decomposition. The Littlewood-Paley operator

is the Fourier inversion of the terms of the sequence. In the classical Littlewood-Paley theory, it is

shown that square root of the sum of squared Littlewood-Paley operator norm over the terms of the

sequence, is bounded on Lebesgue spaces. In this article we will show that the sum is also

bounded on Morrey spaces.

KATA KUNCI : Decomposition function, Littlewood-Paley Theory, and Morrey Space


10/21

Initial Coefficients for Bazilevic Functions in a Sector

SA‘ADATUL FITRI AND MARJONO

Universitas Brawijaya


ABSTRAK

Let be analytic in with , and for and

, l e t , deno te the c lass o f Baz i l e v i c f unc t i ons sa t i s f y i ng

. We studied the initial coefficients for functions in , which unify

and extend well-known results for the class of Bazilevi\v{c} functions. Fekete-Szego

Functional is also solved.

KATA KUNCI : Univalent, Bazilevic functions, Initial Coefficient, Fekete-Szego Functional.

0


On Bounded Topological B-Algebra

ABDUL ROUF ALGHOFARI



ABSTRAK

In this article we present general results on homomorphic images and inverse images in bounded

topological B-algebras.

KATA KUNCI : topology, B-algebra, bounded topology


12/21

Dynamical Systems Analysis of Local and Non-LocalDispersal Models

DR. MOHD HAFIZ MOHD

School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia


ABSTRAK

In this talk, we discuss the effects of different dispersal patterns on the occurrence of priority

effects (alternative stable states) and coexistence in multi-species communities by employing local

(partial-differential equations) and non-local dispersal (integro-differential equations) models. Our

analysis shows the existence of a threshold value in dispersal strength (i.e. saddle-node

bifurcation) above which priority effects disappear. These results also reveal a co-dimension 2

point, corresponding to a degenerate transcritical bifurcation: at this point, the transcritical

bifurcation changes from subcritical to supercritical with corresponding creation of a saddle-node

bifurcation curve.

KATA KUNCI : dispersal patterns, partial-differential equations, integro-differential equations

0


Teorema Titik Tetap untuk Turunan dari Fungsi BernilaiInterval

MOHAMAD MUSLIKH

Jurusan Matematika Universitas Brawijaya


ABSTRAK

Dalam makalah ini ditunjukkan teorema eksistensi titik tetap untuk turunan dari fungsi bernilai

interval. Penyelidikan eksistensi titik tetap tersebut, dalam hal ini, menggunakan metode titik tetap

umum dibawah kondisi kompatibilitas pemetaan komposit hibrid atas metrik Hausdorff. Selain itu

dalam makalah ini diberikan beberapa contoh untuk mendukung kegunaan hasil tersebut.

KATA KUNCI : Teorema titik tetap umum, fungsi bernilai himpunan, pemetaan kompatibel,keterdiferensialan, fungsi bernilai interval

SNAMA 2019 / 12 / ID7 HAMPIRAN

14/21

Perhitungan Kesalahan Deret Cosinus denganKoefisien dari Klas Monoton Umum Orde

MOCH. ARUMAN IMRON

Jurusan Matematika, FMIPA, UB


ABSTRAK

Teorema klasik tentang deret sinus akan konvergen seragam jika koefisien deret tersebut

monoton turun, konvergen ke nol dan juga konvergen ke nol. Himpunan koefisien-koefisien

dengan sifat monoton turun dimasukkan dalam klas MS (Monotone Sequences). Selanjutnya klas

tersebut di generalaisasi menjadi klas GM (General Monotone) dengan syarat deret sinus tetap

konvergen seragam. Mengingat syarat kekonvergenan seragam deret sinus dan perkembangan

klas GM , maka pada makalah ini dikaji kesalahan yang terjadi jika dilakukan pemotongan pada

deret cosinus dengan koefisien dari klas Monoton umum (GM) orde r.

KATA KUNCI : Deret cosinus, Konvergen seragam, Perhitungan kesalahan

0


A Case of Differential Equation with Single StochasticTime Delay

ROBBY1, JALINA WIDJAJA2

1, 2FMIPA Institut Teknologi Bandung


ABSTRAK

In this paper, the behavior of solutions of a linear differential equation with a single stochastic time

delay is investigated. Here we set two possible values of time delay where one value is a multiple

of the other. We assigned a certain distribution to the random variables.

The method of steps is employed to find solutions. The behavior of the solutions is compared to

the behavior of the solution of the corresponding deterministic equations.

The probability of a solution whose value is satisfied with certain conditions is also discussed.

Some simulations using MATLAB are presented.

KATA KUNCI : stochastic time delay, method of step, probability distribution

SNAMA 2019 / 14 / ID11 PERSAMAAN DIFFERENSIAL

16/21

Eksistensi Solusi Lemah untuk Masalah Cauchy-Dirichlet pada Sistem p-Laplacian

CORINA KARIM



ABSTRAK

Dalam penelitian ini akan dipelajari eksistensi solusi lemah untuk sistem parabolik nonlinear pada

persamaan p-Laplacian,

(G)

dengan daerah asal silinder , yang didefinisikan pada himpunan terbuka terbatas

dengan smooth, , dan . Fungsi to

adalah fungsi bernilai vektor yang tidak diketahui dan adalah nilai awal yang berada di

ruang Sobolev . Hasil utama dalam penelitian ini adalah akan dibuktikan eksistensi

solusi lemah untuk persamaan (G) untuk kasus dengan menggunakan metode Galekin.

KATA KUNCI : solusi lemah, kasus degenerate, metode Galerkin

0


Fefferman‘s Inequality and Unique ContinuationProperty of Elliptic Partial Differential Equations

NICKY KURNIA TUMALUN

Institut Teknologi Bandung


ABSTRAK

In this talk, we prove a Fefferman‘s inequality for potentials belonging to a generalized Morrey

space and a Stummel class . Our result extends the previous Fefferman‘s inequality that

was obtained in (2) for the case of Morrey spaces, and that in (4) for the case of Stummel classes,

which was restated recently in (1).

Using this inequality, we prove a strong unique continuation property of a second order elliptic

partial differential equation that generalizes the result in (1) and (4). This is a joint work with Denny

Ivanal Hakim and Hendra Gunawan.

References:

1. Castillo, R.E., Ramos-Fernandez, J., Rojas, E.M.: A note on the Kato class and some

applications. Positivity. 23.2, 327--356 (2019)

2. Chiarenza, F., Frasca, M.: A remark on a paper by C.~Fefferman. Proc. Amer. Math. Soc. {\bf

108}, 407--409 (1990)

3. Fefferman, C.: The uncertainty principle. Bull. Amer. Math. Soc. 9, 129--206 (1983)

4. Zamboni, P.: Some function spaces and elliptic partial differential equations. Le Matematiche

{\bf 42.1. 2}, 171--178 (1987)

KATA KUNCI : Morrey spaces, Stummel classes, Fefferman\‘s inequality, Strong unique continuationproperty.

SNAMA 2019 / 16 / ID30 PERSAMAAN DIFFERENSIAL

18/21

Iterative Operator Splitting Method for A Class ofFisher‘s Equation

DADANG AMIR HAMZAH1, YUDI SOEHARYADI2, JOHAN MATHEUS TUWANKOTTA3

1STT DR KHEZ MUTTAQIEN2, 3Institut Teknologi Bandung


ABSTRAK

This paper is devoted to the study of numerical solution of a class of Fisher‘s equation using

operator splitting method. In particular, the iterative operator splitting method is discussed. This

method splits a difficult problem into several sub-problems which may be easier to solve. Each sub-

problem is solved using a combination of an iterative scheme with suitable integrators.

We carried our analysis by considering the theoretical and numerical aspects. In the theoretical

part, consistency, stability, and convergence of the numerical scheme are discussed. Consistency

analysis is done by considering the boundedness of operators and the choices of initial solutions.

Boundedness of operators plays the main role in deriving the local error by utilizing their nice

properties. However, when the operator is unbounded such nice properties are no longer valid. In

order to derive the local error for the unbounded case, the properties from semigroup theory are

employed. The stability analysis is done by considering the stability with respect to initial condition.

We showed that the change of the solutions with respect to the change of initial conditions are

bounded. The convergence analysis are done using the Lady Windermere‘s Fan argument to relate

the local and the global errors. We showed that the convergence of the scheme by showing that the

global error is bounded. In the numerical part, we apply the scheme to Fisher‘s equation. The

maximum error is observed and then the errors are compared with non iterative operator splitting.

KATA KUNCI : Fisher‘s Equation, Iterative operator splitting method, operator splitting method

0


Aproksimasi Fungsi di dengan Konvolusi

ELIN HERLINAWATI

Universitas Terbuka


ABSTRAK

Konvolusi merupakan operasi matematika pada dua fungsi yang menghasilkan suatu fungsi baru

dan dapat dipandang sebagai versi modifikasi dari salah satu fungsi aslinya. Operasi konvolus tidak

memiliki unsur identitas. Namun, operasi konvolusi memiliki identitas hampiran, yakni dapat

ditemukannya suatu barisan fungsi sehingga konvolusi dari dan konvergen ke untuk

. Hal ini mengakibatkan konvolusi dapat digunakan untuk aproksimasi fungsi. Pada artikel

ini dibuktikan teorema-teorema yang mendasari aproksimasi fungsi dengan konvolusi bagi fungsi di

dengan .

KATA KUNCI : Aproksimasi, fungsi di , konvolusi

SNAMA 2019

20/21

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