Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Boundary condition identification of a bridge pier using experimental data and FEM modal updating

Over the past twenty years, new technologies have required an increasing use of mathematical models in order to understand better the structural behavior: finite element method is the one mostly used. However, the reliability of this method applied to different situations has to be tried each time. Since it is not possible to completely model the reality, different hypothesis must be done: these are the main problems of FE modeling. The following work deals with this problem and tries to figure out a way to identify some of the unknown main parameters of a structure. This main research focuses on a particular path of study and development, but the same concepts can be applied to other objects of research. The main purpose of this work is the identification of unknown boundary conditions of a bridge pier using the data acquired experimentally with field tests and a FEM modal updating process. This work doesn’t want to be new, neither innovative. A lot of work has been done during the past years on this main problem and many solutions have been shown and published. This thesis just want to rework some of the main aspects of the structural optimization process, using a real structure as fitting model.

High-resolution computer simulations of stacking of weak bases using a transient pH boundary in capillary electrophoresis. 1. Concept and impact of sample ionic strength

The dynamics of focusing weak bases using a transient pH boundary was examined via high-resolution computer simulation software. Emphasis was placed on the mechanism and impact that the presence of salt, namely, NaCl, has on the ability to focus weak bases. A series of weak bases with mobilities ranging from 5 x 10(-9) to 30 x 10(-9) m2/V x s and pKa values between 3.0 and 7.5 were examined using a combination of 65.6 mM formic acid, pH 2.85, for the separation electrolyte, and 65.6 mM formic acid, pH 8.60, for the sample matrix. Simulation data show that it is possible to focus weak bases with a pKa value similar to that of the separation electrolyte, but it is restricted to weak bases having an electrophoretic mobility of 20 x 10(-9) m2/V x s or quicker. This mobility range can be extended by the addition of NaCl, with 50 mM NaCl allowing stacking of weak bases down to a mobility of 15 x 10(-9) m2/V x s and 100 mM extending the range to 10 x 10(-9) m2/V x s. The addition of NaCl does not adversely influence focusing of more mobile bases, but does prolong the existence of the transient pH boundary. This allows analytes to migrate extensively through the capillary as a single focused band around the transient pH boundary until the boundary is dissipated. This reduces the length of capillary that is available for separation and, in extreme cases, causes multiple analytes to be detected as a single highly efficient peak.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Does ‘better’ discounting lead to ‘worse’ outcomes in long-run decisions? The dilemma of hyperbolic discounting

The shortcomings of conventional discounting, especially in the context of long-run environmental problems, have been extensively discussed in the literature. Recently, hyperbolic discounting, i. e. discounting at declining instead of constant discount rates, has attracted a lot of interest among both scientists and politicians. Although there are compelling arguments for employing hyperbolic discounting, there are also pitfalls, which have to be pointed out. In this paper I show that the problem of time-inconsistency, an inherent characteristics of hyperbolic discounting, leads to a potential clash between economic efficiency and intergenerational equity. As an example, I refer to the weak progress in the controlling of greenhouse gas emissions under the Kyoto protocol. As the problem of time-inconsistency cannot be solved on economic grounds alone, there is a need for an intergenerational moral commitment.

Evaluation of the diagnostic value of the ELISA tests developed by using EgHF, Em2 and EmII/3-10 antigens in the serological diagnosis of alveolar echinococcosis

Alveolar echinococcosis (AE), caused by larva stage of Echinococcus multilocularis, is one of the lethal parasitic diseases of man and a major public health problem in many countries in the northern hemisphere. When the living conditions and habits in Turkey were considered in terms of relation with the life cycle of the parasite, it was suggested that AE has been much more common than reported mainly from the Eastern Anatolia region of Turkey. Since in vitro serologic diagnosis tests with high specificity for AE have not been used in our country, most of the cases with liver lesions were misdiagnosed by radiological investigations as malignancies. The aim of this study was to evaluate the diagnostic value of the in-house ELISA methods developed by using three different antigens (EgHF, Em2, EmII/3-10) in the serological diagnosis of AE. The study samples included a total of 100 sera provided by Bern University Parasitology Institute where samples were obtained from patients with helminthiasis and all were confirmed by clinical, parasitological and/or histopathological means. Ten samples from each of the cases infected by E.multilocularis, E.granulosus, Taenia solium, Wuchereria bancrofti, Strongyloides stercolaris, Ascaris lumbricoides, Toxocara canis, Trichinella spiralis, Fasciola hepatica and Schistosoma haematobium were studied. In the study, EgHF (E.granulosus hydatid fluid) antigens were prepared in our laboratory from the liver cyst fluids of sheeps with cystic echinococcosis, however Em2 (E.multilocularis metacestode-purified laminated layer) and EmII/3-10 (E.multilocularis recombinant protoscolex tegument) antigens were provided by Bern University Parasitology Institute. Flat bottom ELISA plates were covered with EgHF, Em2 and EmII/3-10 antigens in the concentrations of 2.5 µg, 1 µg and 0.18 µg per well, respectively, and all sera were tested by EgHF-ELISA, Em2-ELISA and EmII/3-10-ELISA methods. For each tests, the samples which were reactive above the cut-off value (mean OD of negative controls+2 SD) were accepted as positive. The sensitivity of the ELISA tests performed with EgHF, Em2 and Em2II/3-10 antigens were estimated as 100%, 90% and 90%, respectively, whereas the specificity were 63%, 91% and 91%, respectively. When Em2-ELISA and EmII/3-10-ELISA tests were evaluated together, the specificity increased to 96%. Our data indicated that the highest sensitivity (100% with EgHF-ELISA) and specificity (96% with Em2-ELISA + EmII/3-10-ELISA) for the serodiagnosis of AE can be achieved by the combined use of the ELISA tests with three different antigens. It was concluded that the early and accurate diagnosis of AE in our country which is endemic for that disease, could be supported by the use of highly specific serological tests such as Em2-ELISA ve EmII/3-10-ELISA contributing radiological data.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Interstellar neutral helium in the heliosphere from Interstellar Boundary Explorer observations. III. Mach number of the flow, velocity vector, and temperature from the first six years of measurements

We analyzed observations of interstellar neutral helium (ISN He) obtained from the Interstellar Boundary Explorer (IBEX) satellite during its first six years of operation. We used a refined version of the ISN He simulation model, presented in the companion paper by Sokol et al. (2015b), along with a sophisticated data correlation and uncertainty system and parameter fitting method, described in the companion paper by Swaczyna et al. We analyzed the entire data set together and the yearly subsets, and found the temperature and velocity vector of ISN He in front of the heliosphere. As seen in the previous studies, the allowable parameters are highly correlated and form a four-dimensional tube in the parameter space. The inflow longitudes obtained from the yearly data subsets show a spread of similar to 6 degrees, with the other parameters varying accordingly along the parameter tube, and the minimum chi(2) value is larger than expected. We found, however, that the Mach number of the ISN He flow shows very little scatter and is thus very tightly constrained. It is in excellent agreement with the original analysis of ISN He observations from IBEX and recent reanalyses of observations from Ulysses. We identify a possible inaccuracy in the Warm Breeze parameters as the likely cause of the scatter in the ISN He parameters obtained from the yearly subsets, and we suppose that another component may exist in the signal or a process that is not accounted for in the current physical model of ISN He in front of the heliosphere. From our analysis, the inflow velocity vector, temperature, and Mach number of the flow are equal to lambda(ISNHe) = 255 degrees.8 +/- 0 degrees.5, beta(ISNHe) = 5 degrees.16 +/- 0 degrees.10, T-ISNHe = 7440 +/- 260 K, nu(SNHe) = 25.8 +/- 0.4 km s(-1), and M-ISNHe = 5.079 +/- 0.028, with uncertainties strongly correlated along the parameter tube.

Determination of sulfite and manganese in sediments from the K/T boundary

The solid-state-physics technique of electron spin resonance (ESR) has been employed in an exploratory study of marine limestones and impact-related deposits from Cretaceous-Tertiary (KT) boundary sites including Spain (Sopelana and Caravaca), New Jersey (Bass River), the U.S. Atlantic continental margin (Blake Nose, ODP Leg 171B/1049/A), and several locations in Belize and southern Mexico within -600 km of the Chicxulub crater. The ESR spectra of SO3(1-) (a radiation-induced point defect involving a sulfite ion substitutional for CO3(2-) which has trapped a positive charge) and Mn(2+) in calcite were singled out for analysis because they are unambiguously interpretable and relatively easy to record. ESR signal strengths of calcite-related SO3(1-) and Mn(2+) have been studied as functions of stratigraphic position in whole-rock samples across the KT boundary at Sopelana, Caravaca, and Blake Nose. At all three of these sites, anomalies in SO3(1-) and/or Mn(2+) intensities are noted at the KT boundary relative to the corresponding background levels in the rocks above and below. At Caravaca, the SO3(1-) background itself is found to be lower by a factor of 2.7 in the first 30,000 years of the Tertiary relative to its steady-state value in the last 15,000 years of the Cretaceous, indicating either an abrupt and quasi-permanent change in ocean chemistry (or temperature) or extinction of the marine biota primarily responsible for fixing sulfite in the late Cretaceous limestones. An exponential decrease in the Mn(2+) concentration per unit mass calcite, [Mn(2+)], as the KT boundary at Caravaca is approached from below (1/e characteristic length =1.4 cm) is interpreted as a result of post-impact leaching of the seafloor. Absolute ESR quantitative analyses of proximal impact deposits from Belize and southern Mexico group naturally into three distinct fields in a twodimensional [SO3(1-)]-versus-[Mn(2+)] scatter plot. These fields contain (I) limestone ejecta clasts, (II) accretionary lapilli, and (III) a variety of SO3(1-) -depleted/Mn(2+) enriched impact deposits. Data for the investigated non-impact-related Cretaceous and Tertiary marine limestones (Spain and Blake Nose) fall outside of these three fields. With reference to thes enon-impact deposits, fields I, II, and III can be respectively characterized as Mn(2+) -depleted, SO3(1-) -enhanced, and SO3(1-) -depleted. It is proposed that (1) field I represents calcites from the Yucatin Platform, and that the Mn(2+) -depleted signature can be used as an indicator of primary Chicxulub ejecta in deep marine environments and (2) field II represents calcites that include a component formed in the vapor plume, either from condensation in the presence of CO2/SO3(1-) -rich vapors, or reactions between CaO and CO2/SO3 rich vapors, and that this SO3(1-) -enhanced signature can be used as an indicator of impact vapor plume deposits. Given these two propositions, the ESR data for the Blake Nose deposits are ascribed to the presence of basal coarse calcitic Chicxulub ejecta clasts, while the finer components that are increasingly represented toward the top are interpreted to contain high- SO3(1-) calcite from the vapor plume. The apparently-undisturbed Bass River deposit may contain even higher concentrations of vapor-plume calcite. None of the three components included in field III appear to be represented at distal, deep marine KT-boundary sites; this field may include several types of impact-related deposits of diverse origins and diagenetic histories.

Stratigraphy of the Campanian-Maastrichtian boundary in ODP Hole 122-762C

An integrated framework of magnetostratigraphy, calcareous microfossil bio-events, cyclostratigraphy and d13C stratigraphy is established for the upper Campanian-Maastrichtian of ODP Hole 762C (Exmouth Plateau, Northwestern Australian margin). Bulk-carbonate d13C events and nannofossil bio-events have been recorded and plotted against magnetostratigraphy, and provided absolute ages using the results of the cyclostratigraphic study and the recent astronomical calibration of the Maastrichtian. Thirteen carbon-isotope events and 40 nannofossil bio-events are recognized and calibrated with cyclostratigraphy, as well as 14 previously published foraminifer events, thus constituting a solid basis for large-scale correlations. Results show that this site is characterized by a nearly continuous sedimentation from the upper Campanian to the K-Pg boundary, except for a 500 kyr gap in magnetochron C31n. Correlation of the age-calibrated d13C profile of ODP Hole 762C to the d13C profile of the Tercis les Bains section, Global Stratotype Section and Point of the Campanian-Maastrichtian boundary (CMB), allowed a precise recognition and dating of this stage boundary at 72.15 ± 0.05 Ma. This accounts for a total duration of 6.15 ± 0.05 Ma for the Maastrichtian stage. Correlation of the boundary level with northwest Germany shows that the CMB as defined at the GSSP is ~800 kyr younger than the CMB as defined by Belemnite zonation in the Boreal realm. ODP Hole 762C is the first section to bear at the same time an excellent recovery of sediments throughout the upper Campanian-Maastrichtian, a precise and well-defined magnetostratigraphy, a high-resolution record of carbon isotope events and calcareous plankton biostratigraphy, and a cyclostratigraphic study tied to the La2010a astronomical solution. This section is thus proposed as an excellent reference for the upper Campanian-Maastrichtian in the Indian Ocean.

Mineralogy and stable oxygen isotope ratios of the Cretaceous-Tertiary boundary

Results of detailed mineralogical, chemical, and oxygen isotope analyses of the clay minerals and zeolites from two Cretaceous-Tertiary (K/T) boundary regions, Stevns Klint, Denmark, and Deep Sea Drilling Project (DSDP) Hole 465A in the north central Pacific Ocean, are presented. In the central part of the Stevns Klint K/T boundary layer, the only clay mineral detected by x-ray diffraction is a pure smectite with > 95 percent expandable layers. No detrital clay minerals or quartz were observed in the clay size fraction in these beds, whereas the clay minerals above and below the boundary layer are illite and mixed-layer smectite-illite of detrital origin as well as quartz. The mineralogical purity of the clay fraction, the presence of smectite only at the boundary, and the d18O value of the smectite (27.2 ± 0.2 per mil) suggest that it formed in situ by alteration of glass. Formation from impact rather than from volcanic glass is supported by its major element chemistry. The high content of iridium and other siderophile elements is not due to the cessation of calcium carbonate deposition and resulting slow sedimentation rates. At DSDP Hole 465A, the principal clay mineral in the boundary zone (80 to 143 centimeters) is a mixed-layer smectite-illite with >=90 percent expandable layers, accompanied by some detrital quartz and small amounts of a euhedral authigenic zeolite (clinoptilolite). The mixed-layer smectite-illite from the interval 118 to 120 centimeters in the zone of high iridium abundance has a very low rare earth element content; the negative cerium anomaly indicates formation in the marine environment. This conclusion is corroborated by the d18O value of this clay mineral (27.1 ± 0.2 per mil). Thus, this mixed-layer smectite-illite formed possibly from the same glass as the K/T boundary smectite at Stevns Klint, Denmark.

Biogenic and mineral composition and foraminiferal stratigraphy of sediment cores obtained in northern Germany

The Ratekau boring ended in clays of the so-called Asterigerina-Zone; these clays have shallow-water features in the uppermost samples. The clays are overlain by deep-water clays with pteropods; this formation is split into two parts by a shallow-water deposit. The fossiliferous series ends upward in sandy deposits with shallow-water fossils. The question is raised whether the two deep-water deposits might correspond to the Lower Doberg Beds (Eochattian) and the Upper Doberg Beds (Neochattian) at the Doberg hill, closer to the rim of the basin. All fossiliferous samples from this boring are thought to be of Late Oligocene age; the boundary towards the Middle Oligocene, however, could not be ascertained. The Vaale boring ended in rather typical Septaria clay of the Middle Oligocene. This clay is capped by some metres of unfossiliferous glauconite clays, which in turn are overlain by silts and silty clays with planktonic fossils identical to those found at Dingden locality. These deposits are tentatively dated as Early Miocene. The next higher series of samples consists of sands and clays deposited in shallower waters. They contain a rich fauna of benthic molluscs, which, according to the current notion in stratigraphy, would have a Reinbek Age. In addition, they contain a set of planktonic fossils which differs from the 'Lower Miocene' assemblages. These sands and clays are overlain by a thick series of marine sands very poor in fossils. Finally, four metres of clay with foraminifera, having Younger Miocene affinities, form the top of the fossiliferous sequence. The borings at Wulksfelde and Langenhorn were not far apart and their sediments are easily correlated. Both wells start below in continental 'Lignite Sands' and contain overlying shallow water sands and clays. These yielded Hemmoor benthic mollusca, supposed to indicate Lower Miocene in the relevant literature; however, we encountered their planktonic foraminifera in the uppermost Miocene as well. The same planktonic species were found in all samples of both borings. These deposits under discussion furthermore contain a particular pteropod species. They are overlain by a thick series of gypsiferous clays, with scarce fossils. The uppermost fossiliferous clays (probably Langenfelde Age) contain another pteropod species, not met with in other samples. The discrepancies between the plankton zonation and the traditional subdivision according to benthic molluscs in the borings of Vaale, Wulksfelde and Langenhorn (and in samples from Twistringen, Dingden and Antwerp localities as well) renders the time-stratigraphic value of the denominations Reinbek and Hemmoor rather doubtful. The samples of the Westerland boring can be placed in the Gram and Sylt stages of local chronostratigraphy on the strength of the Astarte series established by HINSCH. The Gram samples contain a typical pteropod species; both groups of samples contain the same planktonic foraminifera as the borings Wulksfelde and Langenhorn. Our material did not bring the problem of the Miocene-Pliocene boundary in this region any closer to a solution. In conclusion, it can be claimed that this investigation provides strong arguments that the usual recognition of Hemmoor and Reinbek does not correspond to well-defined chronostratigraphical units. A better chronostratigraphic subdivision has to be based on the examination of many more samples, and on a better understanding of the paleoecology of the fossils involved.