| 1. |
- Abylayeva, Akbota
(författare)
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Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis is devoted to investigate weighted differential Hardy inequalities and Hardy-type inequalities with the kernel when the kernel has an integrable singularity, and also the additivity of the estimate of a Hardy type operator with a kernel.The thesis consists of seven papers (Papers 1, 2, 3, 4, 5, 6, 7) and an introduction where a review on the subject of the thesis is given. In Paper 1 weighted differential Hardy type inequalities are investigated on the set of compactly supported smooth functions, where necessary and sufficient conditions on the weight functions are established for which this inequality and two-sided estimates for the best constant hold. In Papers 2, 3, 4 a more general class of -order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < < 1. In Papers 2 and 3 the boundedness and compactness of two classes of such operators are investigated namely of Weyl and Riemann-Liouville type, respectively, in weighted Lebesgue spaces for 1 < p ≤ q < 1 and 0 < q < p < ∞. As applications some new results for the fractional integration operators of Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard are given and discussed.In Paper 4 the Riemann-Liouville type operator with variable upper limit is considered. The main results are proved by using a localization method equipped with the upper limit function and the kernel of the operator. In Papers 5 and 6 the Hardy operator with kernel is considered, where the kernel has a logarithmic singularity. The criteria of the boundedness and compactness of the operator in weighted Lebesgue spaces are given for 1 < p ≤ q < ∞ and 0 < q < p < ∞, respectively. In Paper 7 we investigated the weighted additive estimates for integral operators K+ and K¯ defined byK+ ƒ(x) := ∫ k(x,s) ƒ(s)ds, K¯ ƒ(x) := ∫ k(x,s)ƒ(s)ds.It is assumed that the kernel k of the operators K+and K- belongs to the general Oinarov class. We derived the criteria for the validity of these addittive estimates when 1 ≤ p≤ q < ∞
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| 2. |
- Akhmetkaliyeva, Raya
(författare)
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Maximal regularity of the solutions for some degenerate differential equations and their applications
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis deals with the study of existence and uniqueness together with coercive estimates for solutions of certain differential equations.The thesis consists of six papers (papers A, B, C, D, E and F), two appendices and an introduction, which put these papers and appendices into a more general frame and which also serves as an overview of this interesting field of mathematics.In the text below the functionsr = r(x), q = q(x), m = m(x) etc. are functions on (−∞,+∞), which are different but well defined in each paper. Paper A deals with the study of separation and approximation properties for the differential operator in the Hilbert space (here is the complex conjugate of ). A coercive estimate for the solution of the second order differential equation is obtained and its applications to spectral problems for the corresponding differential operator is demonstrated. Some sufficient conditions for the existence of the solutions of a class of nonlinear second order differential equations on the real axis are obtained.In paper B necessary and sufficient conditions for the compactness of the resolvent of the second order degenerate differential operator in is obtained. We also discuss the two-sided estimates for the radius of fredholmness of this operator.In paper C we consider the minimal closed differential operator in , where are continuously differentiable functions, and is a continuous function. In this paper we show that the operator is continuously invertible when these coefficients satisfy some suitable conditions and obtain the following estimate for : ,where is the domain of .In papers D, E, and F various differential equations of the third order of the form are studied in the space .In paper D we investigate the case when and .Moreover, in paper E the equation (0.1) is studied when . Finally, in paper F the equation (0.1) is investigated under certain additional conditions on .For these equations we establish sufficient conditions for the existence and uniqueness of the solution, and also prove an estimate of the form for the solution of equation (0.1).
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| 3. |
- Kopezhanova, Aigerim
(författare)
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Summability of Fourier transforms of functions from Lorentz spaces
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis is devoted to the study of relations between integrability properties of functions and summability properties of its Fourier coefficients and transforms. The relations are given in terms of generalized weighted Lorentz norms, where the weights have some additional growth properties. The thesis contains six papers (papers A-F) together with an introduction, which put these papers into a general frame.In paper A some relations between weighted Lorentz norms and some corresponding sums of Fourier coefficients are studied for the case with a general orthonormal bounded system. Under certain circumstances even two-sided estimates are obtained.In paper B we study relations between summability of Fourier coefficients and integrability of the corresponding functions for generalized weighted Lorentz spaces in the case of a regular system. Some new inequalities of Hardy-Littlewood-Paley type with respect to a regular system for these generalized Lorentz spaces are obtained. It is also proved that the obtained results are in a sense sharp.In paper C we investigate integrability properties of the orthogonal series with coefficients from generalized weighted Lorentz spaces in the case of a regular system. The upper and the lower estimates of some corresponding Lorentz type norms of the Fourier coefficients are obtained.In paper D some new Boas type theorems for generalized weighted Lorentz spaces with respect to regular systems for generalized monotone functions are proved.In paper E inequalities for the Fourier transform of functions from the generalized weighted Lorentz spaces are studied. The upper and the lower estimates of the norm of the Fourier transform in generalized weighted Lorentz spaces are derived.Finally, in paper F a new inequality concerning the Fourier transform is derived. Moreover, it is described conditions so that this result is sharp in the sense that both upper and lower bounds are obtained.
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| 4. |
- Lintzén, Nina, 1978-
(författare)
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Properties of snow with applications related to climate change and skiing
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Snow has been a subject of research since the mid-20th century. Research on mechanical properties of snow started as an off-shoot of soil mechanics, where methods, tools and instruments used often are the same. However, during the last decades the winter business industry has been growing requiring a number of new fields of research. The aim with this PhD thesis is to investigate and contribute to solutions of some of the new research problems appearing in this area. Machine-made snow is commonly used for buildings and artwork of snow. Only minor scientific studies of machine-made snow and its properties have been published. Therefore, mechanical properties of machine-made snow were investigated. Strength and deformation properties were evaluated through uniaxial compressive tests where cylindrical test specimens were subjected to different constant deformation rates. Creep deformation, bending strength and ultimate load were also evaluated through beam tests. The results showed that the deformation rate is crucial if the snow will deform plastically or if brittle failure will occur. The grain size and structure of the snow had a strong influence on the strength properties. Snow is a constantly changing material with a large variety of grain sizes and shapes. Therefore it is of importance to classify snow. Classication of snow can be done using different methods depending on the property that is to be investigated. Several non-contact detection methods to evaluate snow properties exist. In this thesis, spectral reflectance measurements were performed to investigate liquid water content in snow using two different systems, a spectrometer and an optical sensor called Road Eye. The Road Eye sensor was also used to classify snow in cross-country ski tracks. This method enables a fast classication of a complete track where different types of snow can be distinguished. The properties of a ski track and the characteristics of the snow determine the type of skis that should be selected for optimum sliding properties. Cross-country skis have different mechanical properties, which to a large extent can be evaluated from the span curve of the ski. Depending on the skiing style, the skier's skills, terrain and track conditions different ski properties are required, which is particularly important for competitive skiing. Span curves of cross-country skis were measured using a digital instrument called Skiselector. Results from the investigations showed that skis within the same pair may have signicantly different properties. Moreover, temperature influences the span curve and thus the mechanical properties of the skis. Therefore, skis should be measured at a temperature close to where they are aimed to be used. Field tests of skis with similar span curves but different ski base topography were tested during wet and cold snow conditions. The results indicate that different topographies are preferable during different snow conditions. Due to the climate change, winters have become shorter and warmer with less natural snow. To compensate for the lack of natural snow, ski resorts and other stakeholders produce machinemade snow in order to run their business. Storing snow in insulated piles is an alternative and sometimes a complement to snow production. Studies on stored snow show that the surface area of the pile should be minimized in order to reduce the melt rate. Furthermore, the pileshould be covered with a suciently thick insulating layer, preferably with good evaporation properties. Theoretical calculations can be used to estimate the amount of snow that melts and to predict the efficiency of different materials as thermal insulation on snow. These calculations coincide well with experiments performed in northern Sweden where snow melt was measured. This PhD thesis consists of five publications and an introduction to this area which in particular puts these publications into a more general frame.
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| 5. |
- Nilforoush, Rasoul
(författare)
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Anchorage in Concrete Structures : Numerical and Experimental Evaluations of Load-Carrying Capacity of Cast-in-Place Headed Anchors and Post-Installed Adhesive Anchors
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Various anchorage systems including both cast-in-place and post-installed anchors have been developed for fastening both non-structural and structural components to concrete structures. The need for increased flexibility in the design of new structures and strengthening of existing concrete structures has led to increased use of various metallic anchors in practice. Although millions of fasteners are used each year in the construction industry around the world, knowledge of the fastening technology remains poor. In a sustainable society, buildings and structures must, from time to time, be adjusted to meet new demands. Loads on structures must, in general, be increased to comply with new demands, and the structural components and the structural connections must also be upgraded. From the structural connection point of view, the adequacy of the current fastenings for the intended increased load must be determined, and inadequate fastenings must either be replaced or upgraded. The current design models are generally believed to be conservative, although the extent of this behavior is not very clear. To address these issues, the current models must be refined to allow the design of new fastenings and also the assessment of current anchorage systems in practice.The research presented in this thesis consists of numerical and experimental studies of the load-carrying capacity of anchors in concrete structures. Two different types of anchors were studied: (I) cast-in-place headed anchors, and (II) post-installed adhesive anchors. This research focused particularly on the tensile load-carrying capacity of cast-in-place headed anchors and also on the sustained tension loading performance of post-installed adhesive anchors. The overall objective of this research was to provide knowledge for the development of improved methods of designing new fastening systems and assessing the current anchorage systems in practice.For the cast-in-place headed anchors (I), the influence of various parameters including the size of anchor head, thickness of concrete member, amount of orthogonal surface reinforcement, presence of concrete cracks, concrete compressive strength, and addition of steel fibers to concrete were studied. Among these parameters, the influence of the anchor head size, member thickness, surface reinforcement, and cracked concrete was initially evaluated via numerical analysis of headed anchors at various embedment depths. Although these parameters have considerable influence on the anchorage capacity and performance, this influence is not explicitly considered by the current design models. The numerical results showed that the tensile breakout capacity of headed anchors increases with increasing member thickness and/or increasing size of the anchor head or the use of orthogonal surface reinforcement. However, their capacity decreased considerably in cracked concrete. Based on the numerical results, the current theoretical model for the tensile breakout capacity of headed anchors was extended by incorporating several modification factors that take the influence of the investigated parameters into account. In addition, a supplementary experimental study was performed to verify the numerically obtained findings and the proposed refined model. The experimental results corresponded closely to the numerical results, both in terms of failure load and failure pattern, thereby confirming the validity of the proposed model. The validity of the model was further confirmed through experimental results reported in the literature.Additional experiments were performed to determine the influence of the concrete compressive strength and the addition of steel fiber to concrete on the anchorage capacity and performance. These experiments showed that the anchorage capacity and stiffness increase considerably with increasing concrete compressive strength, but the ductility of the anchor decreases. However, the anchorage capacity and ductility increased significantly with the addition of steel fibers to the concrete mixture. The test results also revealed that the tensile breakout capacity of headed anchors in steel fiber-reinforced concrete is significantly underestimated by the current design model.The long-term performance and creep behavior of the post-installed headed anchors (II) was evaluated from the results of long-time tests on adhesive anchors under sustained loads. In this experimental study, adhesive anchors of various sizes were subjected to various sustained load levels for up to 28 years. The anchors were also exposed to several in-service conditions including indoor temperature, variations in the outdoor temperature and humidity, wetness (i.e., water on the surface of concrete), and the presence of salt (setting accelerant) additives in the concrete. Among the tested in-service conditions, variations in the outdoor temperature and humidity had the most adverse effect on the long-term sustained loading performance of the anchors. Based on the test results, recommendations were proposed for maximum sustained load levels under various conditions. The anchors tested under indoor conditions could carry sustained loads of up to 47% of their mean ultimate short-term capacities. However, compared with these anchors, the anchors tested under outdoor conditions exhibited larger creep deformation and failure occurred at sustained loads higher than 23% of their mean ultimate short-term capacities. Salt additives in concrete and wet conditions had negligible influence on the long-term performance of the anchors, although the wet condition resulted in progressive corrosion of the steel. Based on the experimental results, the suitability of the current testing and approval provisions for qualifying adhesive anchors subjected to long-term sustained tensile loads was evaluated. The evaluations revealed that the current approval provisions are not necessarily reliable for qualifying adhesive anchors for long-term sustained loading applications. Recommendations were given for modifying the current provisions to ensure safe long-term performance of adhesive anchors under sustained loads.
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| 6. |
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| 7. |
- Shambilova, Guldarya, 1977-
(författare)
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Some new Hardy-type inequalities on the cone of monotone functions
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This PhD thesis is devoted to the study weighted Hardy-type inequalitieswith quasilinear integral operators on the cone of monotone functions. Thethesis consists of six papers (papers A - F) and an introduction, which givesa brief review of the theory of Hardy-type inequalities and also serves to putthese papers into a more general frame.In papers A, D and E we characterize some weighted Hardy-type inequal-ities on the cone of non-increasing functions. This problem is related to theboundedness of the Hardy-Littlewood maximal operator in weighted LorentzΓ - spaces. In papers D and E the case with integral operators defined byso called Oinarov’s kernels are treated. In all cases necessary and sufficientconditions are derived.In paper B we solve the similar problem for the cone of quasi-concavefunctions (i.e. when the function f satisfy two monotonicity conditions,namely that f (t) is non-decreasing and f(t)t is non-increasing). Such functions are of great importance for interpolation theory, approximation theory and related areas in functional analysis. Also here complete characterizations are given in all cases.Paper C is devoted to characterizing weighted Hardy-type inequalities with supremum operators on the cone of monotone functions. In particular, the study of the case with non-decreasing functions was initiated in this paper.In paper F we focus only on the much less studied problem, namely to characterize Hardy-type inequalities on the cone of non-decreasing functions. A new reduction method is used in a crucial way. Some complete charac-terizations for all studied cases are discussed and proved. The investigations initiated in paper C are here developed to a more general theory, which cov-ers all studied operators. The obtained results are used to derive some new bilinear Hardy-type inequalities.
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| 8. |
- Tsandzana, Afonso Fernando, 1969-
(författare)
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Homogenization of some new mathematical models in lubrication theory
- 2016
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider mathematical modeling of thin film flow between two rough surfaces which are in relative motion. For example such flows take place in different kinds of bearings and gears when a lubricant is used to reduce friction and wear between the surfaces. The mathematical foundations of lubrication theory is given by the Navier--Stokes equation, which describes the motion of viscous fluids. In thin domains several approximations are possible which lead to the so called Reynolds equation. This equation is crucial to describe the pressure in the lubricant film. When the pressure is found it is possible to predict vorous important physical quantities such as friction (stresses on the bounding surfaces), load carrying capacity and velocity field.In hydrodynamic lubrication the effect of surface roughness is not negligible, because in practical situations the amplitude of the surface roughness are of the same order as the film thickness. Moreover, a perfectly smooth surface does not exist in reality due to imperfections in the manufacturing process. Therefore, any realistic lubrication model should account for the effects of surface roughness. This implies that the mathematical modeling leads to partial differential equations with coefficients that will oscillate rapidly in space and time. A direct numerical computation is therefore very difficult, since an extremely dense mesh is needed to resolve the oscillations due to the surface roughness. A natural approach is to do some type of averaging.In this PhD thesis we use and develop modern homogenization theory to be able to handle the questions above. Especially, we use, develop and apply the method based on the multiple scale expansions and two-scale convergence. The thesis is based on five papers (A-E), with an appendix to paper A, and an extensive introduction, which puts these publications in a larger context.In Paper A the connection between the Stokes equation and the Reynolds equation is investigated. More precisely, the asymptotic behavior as both the film thickness and wavelength of the roughness tend to zero is analyzed and described. Three different limit equations are derived. Time-dependent equations of Reynolds type are obtained in all three cases (Stokes roughness, Reynolds roughness and high frequency roughness regime). In paper C we extend the work done in Paper A where we compare the roughness regimes by numeric computations for the stationary case.In paper B we present a mathematical model that takes into account cavitation, surfaces roughness and compressibility of the fluid. We compute the homogenized coefficients in the case of unidirectional roughness.In the paper D we derive a mathematical model of thin film flow between two close rough surfaces, which takes into account cavitation, surface roughness and pressure dependent density. Moreover, we use two-scale convergence to homogenize the model. Finally, in paper E we prove the existence of solutions to a frequently used mathematical model of thin film flow, which takes cavitation into account.
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