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Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 4) |
| Halaman | : | 1113-1134 |
| Abstrak | : | This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally isotropic Gaussian random field, whose covariance and relation operators are classical pseudodifferential operators. Given the random source, the direct problems are shown to be well-posed in the sense of distributions and the regularity of the solutions are given. For the inverse problems, we demonstrate by ergodicity that the principal symbols of the covariance and relation operators can be uniquely determined by a single realization of the far-field pattern averaged over the frequency band with probability one. |
Evaluasi dan Manajemen Sinkop di Instalasi Gawat Darurat
| Pengarang | : | Sukamto |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 11) |
| Halaman | : | 860-865 |
| Abstrak | : | Syncope is defined as a transient loss of consciousness due to cerebral hypoperfusion, sudden onset, with spon taneous return to baseline function without intervention. It is a common chief complaint in emergency ward. The differential diagnosis for syncope is broad and the management varies significantly depending on the underlying etiology. In the emergen cy department, syncope presents a challenge to general practitioner to differentiate patients safe for discharge from those who require emer gency evaluation and in-hospital management for potentially life-threatening etiologies. |
Metode Diagnostik Dermatitis Kontak Protein
| Pengarang | : | Nyoman Suryawati, Christiana Paramita |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 11) |
| Halaman | : | 855-859 |
| Abstrak | : | rotein contact dermatitis (PCD) is an allergic skin reaction induced principally by proteins of either animal or plant origin. PCD is immediate contact reaction caused by protein of greater molecular weight with possible type 1 immediate hypersensitivity reaction or a combined type 1 and type 4 hypersensitivity reaction. It is important to consider PCD as clinical differential diagnosis of chronic hand dermatitis, especially in high risk occupation contact with protein. Clinical presentation PCD is chronic recurrent dermatitis involving hand and forearms. Prick test is a gold standard test for PCD. The primary step of treatment is avoidance particular allergen and high-potency corticosteroids topical agents. |
Potensi Carvacrol Dalam Daun Bangun-bangun Sebagai Antimikroba dan Imunostimulator
| Pengarang | : | Hilna Khairunisa Shalihat |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 11) |
| Halaman | : | 849-853 |
| Abstrak | : | Coleus amboinicus L is a herbal used mostly in Tanah Karo. It’s ingredient is calvacrol, it is believed to have antimicrobial effect. Experiments showed broad spectrum antimicrobial activity towards Gram positive and Gram negative bacteria; also can act as antifungal. Animal studies showed its potential as immunostimalator. |
Supervised Optimal Transport
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1851-1877 |
| Abstrak | : | Optimal transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan which traditional optimal transport cannot enforce. Here we introduce supervised optimal transport (sOT), which formulates a constrained optimal transport problem where couplings between certain elements are prohibited according to specific applications. sOT is proved to be equivalent to an ????1 penalized optimization problem, from which efficient algorithms are designed to solve its entropy regularized formulation. We demonstrate the capability of sOT by comparing it to other variants and extensions of traditional optimal transport in the color transfer problem. We also study the barycenter problem in sOT formulation, where we discover and prove a unique reverse and portion selection (control) mechanism. Supervised optimal transport is broadly applicable to applications in which a constrained transport plan is involved and the original unit should be preserved by avoiding normalization. |
Generic Convergence to Periodic Orbits for Monotone Flows with Respect to 2-Cones and Applications to SEIRS Models
| Pengarang | : | Lirui Feng |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1829-1850 |
| Abstrak | : | We use a general epidemic model, the SEIRS model with a general nonlinear incidence rate, to show how the recently established generic Poincaré–Bendixson theory of flows monotone with respect to a cone of rank 2 can be used to establish the generic convergence to periodic orbits. Our approach to establishing generic convergence to periodic solutions applies to high-dimensional epidemic systems and predator-prey systems, very much like the generic convergence to equilibria in cooperative systems using the classical monotone dynamical systems theory. |
Nematic Liquid Crystals in a Rectangular Confinement: Solution Landscape, and Bifurcation
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1808-1828 |
| Abstrak | : | We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau–de Gennes framework in terms of two geometry-dependent variables: half short edge length ???? and aspect ratio ???? . First, we analytically prove that, for any ???? with a small enough ???? or for a large enough ???? with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying ???? and ???? , and report a novel X state, which emerges from saddle-node bifurcation and serves as the parent state in such a solution landscape. Various new classes are then found among these solution landscapes, including the X class, the S class, and the L class. By tracking the Morse indices of individual solutions, we present bifurcation diagrams for nematic equilibria, thus illustrating the emergence mechanism of critical points and several effects of geometrical anisotropy on confined defect patterns. |
Robustness of Solutions of Almost Every System of Equations
| Pengarang | : | Sana Jahedi |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1791-1807 |
| Abstrak | : | In mathematical modeling, it is common to have an equation ?????(????) =???? , where the exact form of ???? is not known. This article shows that there are large classes of ???? where almost all ???? share the same properties. The classes we investigate are vector spaces F of ????1 functions ???? :????? →????? that satisfy the following condition: F has “almost constant rank" (ACR) if there is a constant integer ?????(F) ≥0 such that rank (??????????(????)) =?????(F) for “almost every" ???? ∈F and almost every ???? ∈????? . If the vector space F is finite dimensional, then “almost every" is with respect to the Lebesgue measure on F , and otherwise, it means almost every in the sense of prevalence, as described herein. Most function spaces commonly used for modeling purposes are ACR. In particular, we show that if all of the functions in F are linear or polynomial or real analytic, or if F is the set of all functions in a “structured system", then F is ACR. For each ???? and ???? , the solution set of ???? ∈????? is SolSet (????) :={???? :?????(????) =?????(????)} . A solution set of ?????(????) =???? is called robust if it persists despite small changes in ???? and ???? . The following two global results are proved for almost every ???? in an ACR vector space F : (1) Either the solution set SolSet (????) is robust for almost every ???? ∈????? , or none of the solution sets are robust. (2) The solution set SolSet (????) is a ????∞ -manifold of dimension ???? =???? −?????(F) . In particular, ???? is the same for almost every ???? ∈F . |
Sparse Optimal Control of Pattern Formations for an SIR Reaction-Diffusion Epidemic Model
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1764-1790 |
| Abstrak | : | Pattern formation arising from the reaction-diffusion epidemic model is a space-time depiction of the distribution and transmission of infectious diseases. Disease control can be achieved by controlling the associated pattern formations. For an SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates under the case of a constant recovery rate. To control pattern formations of the SIR epidemic model, we introduce a regulator as a control function of the recovery rate. For a perfect control strategy, it not only leads to a desired pattern formation, but also has a small support in space-time domains. In order to obtain such a control strategy, we propose a sparse optimal control problem governed by the SIR epidemic model. We study the existence of optimal solutions, derive the first order necessary optimality system, obtain the sparsity structure of the control function, and numerically solve the control problem. Numerical results demonstrate the feasibility and effectivity of our method. |
Standing Waves of Reaction-Diffusion Equations on an Unbounded Graph with Two Vertices
| Pengarang | : | Satoru Iwasaki |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 5) |
| Halaman | : | 1733-1763 |
| Abstrak | : | We deal with bistable reaction-diffusion equations in a domain of a metric graph with two vertices, that is, a domain of multiple half-lines with two junctions connected by a line segment. We prove that there exist two types of standing waves: standing front waves and unimodal waves, if the line segment is long enough. We also numerically show the exact number of standing wave solutions for a cubic nonlinearity and for a piecewise linear case. The stability and instability of the standing wave solutions are also investigated. Standing waves play a role in blocking the front propagation. |