Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis

Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.

Snakebites as a largely neglected problem in the Brazilian Amazon: highlights of the epidemiological trends in the State of Amazonas

Envenoming snakebites are thought to be a particularly important threat to public health worldwide, especially in rural areas of tropical and subtropical countries. The true magnitude of the public health threat posed by snakebites is unknown, making it difficult for public health officials to optimize prevention and treatment. The objective of this work was to conduct a systematic review of the literature to gather data on snakebite epidemiology in the Amazon region and describe a case series of snakebites from epidemiological surveillance in the State of Amazonas (1974-2012). Only 11 articles regarding snakebites were found. In the State of Amazonas, information regarding incidents involving snakes is scarce. Historical trends show an increasing number of cases after the second half of the 1980s. Snakebites predominated among adults (20-39 years old; 38%), in the male gender (78.9%) and in those living in rural areas (85.6%). The predominant snake envenomation type was bothropic. The incidence reported by the epidemiological surveillance in the State of Amazonas, reaching up to 200 cases/100,000 inhabitants in some areas, is among the highest annual snakebite incidence rates of any region in the world. The majority of the cases were reported in the rainy season with a case-fatality rate of 0.6%. Snakebite envenomation is a great disease burden in the State of Amazonas, representing a challenge for future investigations, including approaches to estimating incidence under-notification and case-fatality rates as well as the factors related to severity and disabilities.

Retrieval of kinetic rates in reactions with semi batch liquid phase using ill-posed inverse problem theory

A neural network procedure to solve inverse chemical kinetic problems is discussed in this work. Rate constants are calculated from the product concentration of an irreversible consecutive reaction: the hydrogenation of Citral molecule, a process with industrial interest. Simulated and experimental data are considered. Errors in the simulated data, up to 7% in the concentrations, were assumed to investigate the robustness of the inverse procedure. Also, the proposed method is compared with two common methods in nonlinear analysis; the Simplex and Levenberg-Marquardt approaches. In all situations investigated, the neural network approach was numerically stable and robust with respect to deviations in the initial conditions or experimental noises.

Evaluation of the problem posed by in-place pollutants in Baltimore Harbor and recommendation of corrective action.

Mode of access: Internet.

A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

The problem posed by exam choice on the comparability of results in the Finnish matriculation examination

The article focuses on the upper secondary matriculation examination in Finland as a school leaving and university entrance examination. The presented research addresses the question of whether increased choice of the subject-specific examinations has the potential to undermine the comparability of examination results and to direct students’ choices not only in the examination but already beforehand at school. The authors refer to Finland’s tradition of more than 160 years of a national examination connecting the academic track of upper secondary schools with universities. The authors explain the Finnish system by describing the adoption of a course-based (vs. class- or year-based) curriculum for the three-year upper secondary education and the subsequent reforms in the matriculation examination. This increases students’ choices considerably with regard to the subject-specific exams included in the examination (a minimum of four). As a result, high-achieving students compete against each other in the more demanding subjects while the less able share the same normal distribution of grades in the less demanding subjects. As a consequence, students tend to strategic exam-planning, which in turn affects their study choices at school, often to the detriment of the more demanding subjects and, subsequently, of students’ career opportunities, endangering the traditional national objective of an all-round pre-academic upper secondary education. This contribution provides an overview of Finnish upper secondary education and of the matriculation examination (cf. Klein, 2013) while studying three separate but related issues by using data from several years of Finnish matriculation results: the relation of the matriculation examination and the curriculum; the problems of comparability vis-à-vis university entry due to the increased choice within the examination; the relations between students’ examination choices and their course selection and achievement during upper secondary school. (DIPF/Orig.)

Numerical solution of an elliptic 3-dimensional Cauchy problem by the alternating method and boundary integral equations

We consider the Cauchy problem for the Laplace equation in 3-dimensional doubly-connected domains, that is the reconstruction of a harmonic function from knowledge of the function values and normal derivative on the outer of two closed boundary surfaces. We employ the alternating iterative method, which is a regularizing procedure for the stable determination of the solution. In each iteration step, mixed boundary value problems are solved. The solution to each mixed problem is represented as a sum of two single-layer potentials giving two unknown densities (one for each of the two boundary surfaces) to determine; matching the given boundary data gives a system of boundary integral equations to be solved for the densities. For the discretisation, Weinert's method [24] is employed, which generates a Galerkin-type procedure for the numerical solution via rewriting the boundary integrals over the unit sphere and expanding the densities in terms of spherical harmonics. Numerical results are included as well.

Crystal engineering strategies against antimicrobial resistance: a solid contribution to a contemporary problem

This PhD thesis sets its goal in the application of crystal engineering strategies to the design, formulation, synthesis, and characterization of innovative materials obtained by combining well established biologically active molecules and/or GRAS (generally recognized as safe) compounds with co-formers able to modulate specific properties of the molecule of interest. The solid-state association, via non-covalent interactions, of an active ingredient with another molecular component, a metal salt or a complex, may alter in a useful way the physicochemical properties of the active ingredient and/or may allow to explore new ways to enhance, in a synergistic way, the overall biological performance. More specifically this thesis will address the threat posed by the increasing antimicrobial resistance (AMR) developed by microorganisms, which call for novel therapeutic strategies. Crystal engineering provides new tools to approach this crisis in a greener and cost-effective way. This PhD work has been developed along two main research lines aiming to contribute to the search for innovative solutions to the AMR problem. Design, preparation and characterization of novel metal-based antimicrobials, whereby organic molecules with known antimicrobial properties are combined with metal atoms also known to exert antimicrobial action. Design, preparation and characterization of co-crystals obtained by combining antibacterial APIs (active pharmaceutical ingredients) with natural antimicrobials.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

This paper addresses the capacitated lot sizing problem (CLSP) with a single stage composed of multiple plants, items and periods with setup carry-over among the periods. The CLSP is well studied and many heuristics have been proposed to solve it. Nevertheless, few researches explored the multi-plant capacitated lot sizing problem (MPCLSP), which means that few solution methods were proposed to solve it. Furthermore, to our knowledge, no study of the MPCLSP with setup carry-over was found in the literature. This paper presents a mathematical model and a GRASP (Greedy Randomized Adaptive Search Procedure) with path relinking to the MPCLSP with setup carry-over. This solution method is an extension and adaptation of a previously adopted methodology without the setup carry-over. Computational tests showed that the improvement of the setup carry-over is significant in terms of the solution value with a low increase in computational time.

GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.