This work demonstrated that the coupling of supercritical carbon dioxide extraction with slow pyrolysis is effective to remove over half of extractives from low quality wood and to generate biochar from remaining solid wood fractions. The high yields of extractives from supercritical carbon dioxide extraction illustrates the potential utilizing of low quality wood as an alternative feedstock for the sustainable production of value-added chemicals. Results showed that supercritical carbon dioxide extraction has neither a strong impact on the physical properties of original wood nor on the yield of solid biochar. These results are promising as they show that the biochar obtained for this renewable feedstock could be used as an alternative to fossil-based coke in applications including ferroalloy industries. Moreover, the heat treatment temperature and supercritical carbon dioxide extraction had a significant impact on the tar yields, leading to the increase in naphthalene, polycyclic aromatic hydrocarbons, aromatic and phenolic fractions with the greater temperature. The differences in gasification reactivity and dielectric properties of solid biochars, composition and yields of liquid products of non-treated pinewood and extracted wood fraction emphasize the impact of supercritical carbon dioxide extraction on the pyrolysis process. 

In this work, small signal DC voltage dependent dielectric permittivity, loss tangent, and tuneability of magnetron sputtered epitaxial Na0.5K0.5NO3 films are studied experimentally. (100)-oriented Na0.5K0.5NbO3 films are deposited onto SiO2-buffered CMOS grade low resistivity (p = 10-20 cm) and high resistivity (p = 15-45 kcm) silicon substrates. Planar capacitors with 2 or 4 m gaps between electrodes have been fabricated on top of ferroelectric films. These devices have been characterized in the frequency range 1.0 MHz to 50 GHz at temperatures 30 - 300K. Na0.5K0.5NbO3/SiO2/Si structures on high resistivity silicon substrate exhibit C-V performances typical for Metal-Insulator- Semiconductor (MIS) capacitors. At low frequencies, f 1.0 GHz, the large tuneability and large losses are associated with the MIS structure, while at higher microwave frequencies the tuneability is mainly associated with the ferroelectric, film. At 1.0 MHz and room temperature, the tuneability of Na0.5K0.5NbO3/SiO2/Si structures more than 90%, reducing to 10-15 % at 50 GHz. The losses decrease with increasing the DC bias and frequency. A Q-factor more than 15 at 50 GHz is observed. The dielectric permittivity of the Na0.5K0.5NbO3 film is in the range 50-150 at frequencies 0.045-50 GHz. On low resistivity substrate the performance of Na0.5K0.5NbO3 films is completely screened by the high losses in silicon, and the tuneability is negligible

Wear is a significant challenge encountered in the mining industry, affecting the durability and performance of materials. Hadfield steel has emerged as a commonly used material in this field due to its favorable properties. However, there is a persistent need to enhance its service life. Metal matrix composites (MMCs) offer a potential solution to address this issue. By reinforcingHadfield steel with ceramic particles, MMCs aim to improve the material's wear resistance and extend its operational lifespan. This study specifically investigates the potential of MMCs, reinforced with Zirconia Toughened Alumina (ZTA) particles, to enhance the performance of Hadfield steel in mining applications. Notably, ZTA particles are chosen for their exceptional wear resistance and low cost, making them an attractive reinforcement option. The mechanical behavior and properties of ZTA particle reinforced metal matrix composites (MMCs) were thoroughly investigated by conducting a comprehensive analysis. This analysis encompassed adetailed examination of the microstructure, composition, distribution, as well as the bonding between ZTA particles and the metallic matrix, along with rigorous measurements of hardness and wear resistance. The findings of the study reveal that the ZTA particle reinforced MMCs exhibit a uniform dispersion of ZTA particles throughout the composite material. This homogeneous distribution contributes to notable enhancements in the average hardness of the MMCs, surpassing that of Hadfield steel alone. However, the study did not observe a substantial enhancement in the wear resistance of the material.

Recently, triboelectric nanogenerators (TENGs) have been widely used for energy harvesting and self-powered sensing due to their significant and unique advantages. However, the intrinsic mechanisms that contribute to tribo-electricification (TE) between two materials remain as a subject of rigorous debate. In addition to predicting the qualitative charge transfer in solid-solid contacts based on the difference in the work functions of the two moieties constituting the interface, we argue that it is essential to obtain atomic-level, first principles, insights into the bonding properties, quantitative charge transfer, and the possible presence of a electrostatic potential barrier at the interface to fully understand the TE mechanism of a system. We have utilized dispersion-corrected density functional theory (DFT) calculations in this study to systematically investigate the TE potential of bare surface Ti3C2 and Ti3N2 2D MXene monolayers and their surface functionalized modifications Ti3C2R2 and Ti3N2R2 (where R = -O, -OH, or -F) in contact with Al(111). For these heterostructures, we have analyzed the adhesive energy of the interfaces, the nature of interaction through the electron localization function (ELF), and the charge distribution, which have revealed distinct characteristics of MXene/Al contacts for these monolayer/metal interfaces at their equilibrium distance and the changes in their properties under uniaxial pressure. Among all the metallic 2D MXene variants investigated in this study, we have determined that Ti3C2F2/Al and Ti3N2F2/Al interfaces show exceptional potential for TE.

In the present work, we investigate, for the first time, quasi 3D porous tetragonal silicon–carbon polymorphs t(SiC)₁₂ and t(SiC)₂₀ on the basis of first-principles density functional theory calculations. The structural design of these q3-t(SiC)12 and q3-t(SiC)₂₀ polymorphs follows an intuitive rational approach based on armchair nanotubes of a tetragonal SiC monolayer where C–C and Si–Si bonds are arranged in a paired configuration for retaining a 1:1 ratio of the two elements. Our calculations uncover that q3-t(SiC)₁₂ and q3-t(SiC)₂₀ polymorphs are thermally, dynamically, and mechanically stable with this lattice framework. The results demonstrate that the smaller polymorph q3-t(SiC)₁₂ shows a small band gap (∼0.59 eV), while the larger polymorph of q3-t(SiC)₂₀ displays a Dirac nodal line semimetal. Moreover, the 1D channels are favorable for accommodating Na ions with excellent (>300 mAh g^–1) reversible theoretical capacities. Thus confirming potential suitability of the two porous polymorphs with an appropriate average voltage and vanishingly small volume change (<6%) as anodes for Na-ion batteries.

Heterostructures offer superior photocatalytic characteristics over their constituent counterparts due to their charge separation abilities. Here, we conduct a systematic study of a recently synthesized novel family of palladium-based pentagonal air-stable 2D monolayers, PdSe₂, PdPSe, and PdPS, and their heterostructures using first-principles calculations for photocatalytic applications. Electronic band structure calculations reveal moderate bandgaps of 2.27 eV for PdSe2, 2.01 eV for PdPSe, and 2.25 eV for PdPS, indicating their suitability for photocatalytic water splitting. Moreover, to spatially separate and reduce the recombination possibility of photoinduced electron-hole pairs, we propose three van der Waals heterostructures: PdPSe/PdSe₂, PdPS/PdSe₂, PdPS/PdPS, with the corresponding bandgaps of 1.84 eV, 1.64 eV, and 1.65 eV, respectively. Based on work functions and the staggered band alignment of constituting monolayers, all three heterostructures are identified as type-II photocatalysts, which makes them notable photocatalyst. Additionally, band-edge potentials of PdPSe/PdSe₂ and PdPS/PdSe₂ confirm their suitability for overall water splitting via photocatalysis, whereas PdPS/PdPSe is suitable for oxygen evolution reactions only. The optical absorption spectra show the ability of each system to operate under a wide range of the spectrum, from visible light to high-energy (UV) regions. These characteristics make these systems valuable and attractive for photocatalytic applications.

The mechanical, thermodynamic, electronic, and optical properties of Na₂MoO₄ (NMO) and Na₂WO₄ (NWO) spinels are elaborated by density functional theory (DFT) based full potential augmented plane wave method (FP-LAPW + lo). Our optimized lattice constants for the studied spinels are in good agreement with that obtained experimentally. The enthalpy of formation ensures the thermodynamic stability of NMO and NWO in the cubic phase. The Born mechanical stability criteria guarantees their mechanical stability, while Poisson ratio (ν) and Pugh's ratio (B/G) infer their brittle behavior. The Debye temperature (θ_D) is significant for NMO than NWO. The wide bandgap of 3.5 eV for NMO and 4.4 eV for NWO show the maximum absorption in the ultraviolet region that increases their importance for optoelectronic applications. The optical properties are explained in term of dielectric constant, refractive index, absorption of light, reflection, and optical loss factor.

We consider a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding between the spaces with multiweighted derivatives in different selections of weights.

This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we consider and analyze some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we present and prove analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are crucially for the proofs of the main results of this Licentiate Thesis. In Chapter 3 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of spaces. However, with the help of our new embedding theorems we can extend these results to the case of strong degeneration. In Chapter 4 we prove some new estimates for each function in a Tchebychev system. In order to be able to study also compactness of the embeddings from Chapter 3 such estimates are crucial. I plan to study this question in detail in my further PhD studies.

This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.

We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n

This thesis has investigated the techno-economic feasibility of upgrading the sludge from a chemical pulp mill to hydrochar via hydrothermal carbonization (HTC). The intended use of the hydrochar was to replace fossil coal within metallurgical applications in the iron and steel industry.

Process models were developed in order to obtain mass and energy balances of the HTC process for different technical configurations. The balances were used to evaluate the economic performance, in terms of hydrochar production cost as well as different profitability parameters. Two main scenarios were investigated:

Scenario-1: HTC process integrated with the pulp millScenario-2: Stand alone HTC process.To see the effect of having one or two HTC reactors, two cases were developed for each scenario, where the first case used only mixed sludge from the pulp mill as feedstock for the HTC process (case 1, one reactor), while the second case used both mixed sludge and bark as feedstock (case 2, two reactors).

In scenario 1, the effects on the pulp mill’s mass and energy balances of integrating the HTC process were investigated. The results showed only very small impacts on the pulp mill, due to that the HTC process is significantly smaller than the mill. The total amount of steam to the steam turbine increased by 0.8 % and 0.9 %, for case 1 and 2, respectively. In combination with the removed sludge, which is otherwise combusted in the mill’s socalled power boiler, this entailed a total increase of the wood fuel consumption in the boiler by 3.2 % and 3.6 %, respectively.

By implementing a second HTC reactor, the production cost of hydrochar could in the integrated scenario (scenario 1) be decreased from 4 600 SEK/ton (case 1) to 3 700 SEK/ton (case 2). The corresponding production costs in the stand alone scenario (scenario 2) amounted to 5 400 SEK/ton (case 1) and 4 200 SEK/ton (case 2), respectively. Both integration with the pulp mill and increasing the HTC production scale were thus found to be strategies that can lead to decreased hydrochar production cost. However, even the lowest production cost noted in this report is significantly higher than the corresponding price of coal. This indicates that other measures are required in order for hydrochar to become cost competitive to fossil coal in the metallurgical industry. Examples are the possibility to use even lower-cost feedstocks, as well as policy tools targeting, e.g., the CO₂ emissions from using fossil materials and energy carriers in the iron and steel industry.

Based on the results from the investment calculation, it is concluded that the HTC process integrated with a pulp mill is preferable compared to a stand alone HTC process. The reason why integrated HTC is preferred is that it gives higher NPV and correspondingly lower payback time, as well as lower hydrochar production costs.

Advent of power electronic switching is introducing more and more non-linear loads in the low voltage grid. Besides harmonic current generation in the frequency range below 2 kHz, these non-linear loads are also responsible for current emission in the range of 2 kHz to 150 kHz, commonly known as supraharmonic emission. Supraharmonic currents mainly flow between nearby appliances and heavily influence the overall emission of neighboring devices. This paper presents an analysis of supraharmonic interaction between a photovoltaic inverter and an electric vehicle. It has been noticed that intermodulation distortion arises as a result of interaction between different switching frequencies used by the devices. Later, additional household equipment were added to photovoltaic and electric vehicle to observe their effect on intermodulation distortion. All the measurements were conducted in a controlled laboratory environment imitating a domestic customer.

Ductile fracture presents challenges with respect to material modelling andnumerical simulations of localization. The strain and damage localization maybe unwanted as it indicates a failure in the process or, as in the case ofmachining and cutting, a wanted phenomenon to be controlled. The latterrequires a higher accuracy regarding the modelling of the underlying coupledplastic and fracturing/damage behaviour of the material, metal in the currentcontext as well as the stability and robustness of the simulation procedure.This aim of this work is to develop, evaluate and implement formulations thatcan efficiently and reliably handle localization problems in machiningsimulations. The focus is on non-local models. The non-local models extendthe standard continuum mechanics theory by using non-local continuumtheory in order to achieve mesh independent results when simulating fractureor shear localization.The non-local damage model is implemented and various formulations areevaluated in a Matlab™ based finite element code. The chosen algorithm wasthen implemented in commercial software. The implementations remedy themesh sensitivity problem and gives convergent solution for metal cuttingsimulations with reasonable cost. The length scale associated with the nonlocalmodels are in the current context considered as a numericalregularization parameter. The model has been applied in machiningsimulations and compared with measurements from industry.Keywords: Finite element simulation; Non-local damage; Plasticity; Machining

Ductile fracture presents challenges with respect to material modelling and numerical simulations of localization. The strain and damage localization may be unwanted as it indicates a failure in the process or, as in the case of machining and cutting, a wanted phenomenon to be controlled. The latter requires a higher accuracy regarding the modelling of the underlying coupled plastic and fracturing/damage behaviour of the material, metal in the current context as well as the robustness of the simulation procedure. The focus of this thesis is on efficient and reliable finite element solution of the localization problem through the non-local damage model. The non-local damage model extends the standard continuum mechanics theory by using non-local continuum theory in order to achieve mesh independent results when simulating fracture or shear localization. In this work, the non-local damage model and its various simplifications are evaluated in an in-house finite element code developed using Matlab™. The accuracy, robustness, efficiency and costs of the models are investigated and also compared to a general multi-length scale finite element formulation. A numerical study versus published data is used to demonstrate the validity of the model. The explicit non-local damage variant will be implemented in a commercial finite element code for use in machining simulation

Localisation of deformation is a problem in several manufacturing processes. Machining is an exception where it is a wanted feature. However, it is always a problem in finite element modelling of these processes due to mesh sensitivity of the computed results. The remedy is to incorporate a length scale into the numerical formulations in order to achieve convergent solutions. Different simplifications in the implementation of a non-local damage model are evaluated with respect to temporal and spatial discretisation to show the effect of different approximations on accuracy and convergence.

Localisation of deformation is a problem in several manufacturing processes. Machining is an exception where it is a wanted feature. However, it is always a problem in finite element modelling of these processes due to mesh sensitivity of the computed results. The remedy is to incorporate a length scale into the numerical formulations in order to achieve convergent solutions. Different simplifications in the implementation of a non-local damage model are evaluated with respect to temporal and spatial discretisation to show the effect of different approximations on accuracy and convergence.

Modelling and simulation of manufacturing processes may require the capability to account for localization behavior, often associated with damage/fracture. It may be unwanted localization indicating a failure in the process or, as in the case of machining and cutting, a wanted phenomenon to be controlled. The latter requires a higher accuracy regarding the modelling of the underlying physics, as well as the robustness of the simulation procedure. Two different approaches for achieving mesh-independent solutions are compared in this paper. They are the multiresolution continuum theory (MRCT) and nonlocal damage model. The MRCT theory is a general multilength-scale finite element formulation, while the nonlocal damage model is a specialized method using a weighted averaging of softening internal variables over a spatial neighborhood of the material point. Both approaches result in a converged finite element solution of the localization problem upon mesh refinement. This study compares the accuracy and robustness of their numerical schemes in implicit finite element codes for the plane strain shear deformation test case. Final remarks concerning ease of implementation of the methods in commercial finite element packages are also given.

One of the aims of this work is to show that thermal softening due to the reduced flow strength of a material with increasing temperature may cause chip serrations to form during machining. The other purpose, the main focus of the paper, is to demonstrate that a non-local temperature field can be used to control these serrations. The non-local temperature is a weighted average of the temperature field in the region surrounding an integration point. Its size is determined by a length scale. This length scale may be based on the physics of the process but is taken here as a regularization parameter.

Non-local damage model for strain softening in a machining simulation is presented in this paper. The coupled damage-plasticity model consists of a physically based dislocation density model and a damage model driven by plastic straining in combination with the stress state. The predicted chip serration is highly consistent with the measurement results. 

Converter-fed railway power systems traditionally use high voltage AC overhead transmission lines in the railway grid for increased loadability. An increased resistance to overhead high voltage AC transmission lines, may motivate cables as one alternative for the future. The focus of this paper is to compare a non-strengthened system with two cable solutions for comparing loadability, voltages, and reactive powers for different levels of load scaling. The studies confirmed that the obstacle of reactive power produced in lowly utilized cables is, even if less significant for low frequency AC, still present. A simplified load model is used representing trains with VSC-converters and three-phase motors as purely active loads regardless of motoring or regenerating. A previous study has been done on thyristor-based trains. The voltage levels while regenerating are higher than in the thyristor-train case study. Besides that the loadability for motoring and regenerating is higher with modern VSC-trains.

n railway power supply systems using ACfrequencies lower than the public grids of 50/60 Hz,high voltage AC overhead transmission lines in railwaygrid frequency are used as one measure of strengthen-ing the systems. An increased resistance to overheadhigh voltage AC transmission lines, may motivate ca-bles for future railway power systems.With the frequency of 50/60 Hz, reactive powerproduced in lowly utilized cables imposes an obstacle.For low frequency AC, this issue is less significant.Moreover, in converter-fed railways, no reactive powerwill leak into the feeding public grid.This paper studies AC cables in low-frequency ACrailway. Two reinforcement cable solutions are com-pared with no reinforcement. A simplified load model oftrains, with thyristor bridges and DC motors, is used

Conventional compensation circuits for phase balancing of single phase AC railways for 50 or 60 Hz have high cost for the associated transformers. A new version of the classical Steinmetz scheme, using three single phase transformers connected as a W with the phase angles -60°, 0° and +60°, can reuse the two standard single phase transformers of a V-connected feeding station with a third identical transformer added. Power factor compensation can easily be included. For neutral sections between different feeding systems, a neutral section converter is proposed.

Conventional compensation circuits for phase balancing of single phase AC railways for 50 or 60 Hz have high cost for the associated transformers. A new version of the classical Steinmetz scheme, using three single phase transformers connected as a W with the phase angles -60°, 0° and +60°, can reuse the two standard single phase transformers of a V-connected feeding station with a third identical transformer added. Power factor compensation can easily be included. For neutral sections between different feeding systems, a neutral section converter is proposed.

This paper continues the pursuit of getting a deeper understanding regarding the transient stability of low-frequency AC railway power systems operated at 16 2/3 Hz synchronously to the public grid. The focus is set on the impact of different load models. A simple constant-current load model is proposed and compared to a previously proposed and studied load model in which the train’s active power is regulated.

The study and comparison is made on exactly the same cases as and grid as with the already proposed and more advanced load model. The railway grid is equipped with a low-frequency AC high-voltage transmission line which is subjected to a fault. The study is limited to railways being fed by different distributions of RFC (Rotary Frequency Converter) types. Both AT (auto transformer) and BT (booster transformer) catenaries are considered.

The RFC dynamic models are essentially Anderson-Fouad models of two synchronous machines coupled mechanically by their rotors being connected to the same shaft.

The differences in load behaviour between the proposed constant-current load model and the previously proposed and studied voltage-dependent active power load model are analyzed and described in the paper.

This paper continues the pursuit of getting a deeper understanding regarding the transient stability of low-frequency AC railway power systems operated at 16 2/3 Hz that are synchronously connected to the public grid. Here, the focus is set on such grids with a low-frequency AC high-voltage transmission line subject to a fault. The study here is limited to railways being fed by different distributions of Rotary Frequency Converter (RFC) types. Both auto transformer (AT) and booster transformer (BT) catenaries are considered. No mixed model configurations in the converter stations (CSs) are considered in this study. Therefore, only interactions between RFCs in different CSs and between RFCs, the fault, and the load can take place in this study. The RFC dynamic models are essentially two Anderson-Fouad models of synchronous machines coupled mechanically by their rotors being connected to the same mechani- cal shaft. Besides the new cases studied, also a new voltage-dependent active power load model is presented and used in this study.

In present-day railway power supply systems using an AC frequency lower than the one in the public power system of 50/60 Hz, high voltage overhead transmission lines are used as one measure of strengthening the railway power supply system grids. This option may be economically beneficial, compared to strengthening the grid purely by increasing the density of converter stations or increasing the cross section areas of the overhead catenary wires. High voltage AC transmission lines in the railway power supply system allow larger distances between converter stations than would otherwise be possible for a given amount of train traffic. Moreover, the introduction of AC transmission lines implies reduced line losses and reduced voltage level fluctuations at the catenary for a given amount of train traffic. However, due to the increased public and government resistance for additional overhead high voltage AC transmission lines in general, different alternatives will be needed for the future improvements and strengthening of railway power systems. For a more sustainable transport sector, the share and amount of railway traffic needs to increase, in which case such a strengthening becomes inevitable. Earlier, usage of VSC-HVDC transmission cables has been proposed as one alternative to overhead AC transmission lines. One of the main benefits with VSC-HVDC transmission is that control of power flows in the railway power systems is easier and that less converter capacity may be needed. Technically, VSC-HVDC transmission for railway power systems is a competitive solution as it offers a large variety of control options. However, there might be other more economical alternatives reducing the overall impedance in the railway power system. In public power systems with the frequency of 50/60 Hz, an excess of reactive power production in lowly utilized cables imposes an obstacle in replacing overhead transmission lines with cables. In low frequency AC railway power system, the capacitive properties are less significant allowing longer cables compared to 50/60 Hz power systems. Moreover, in converter-fed railways, some kind of reactive compensation will automatically be applied during low-load. At each converter station, voltage control is already present following the railway operation tradition. Therefore, in this paper, we propose AC cables as a measure of strengthening low-frequency AC railway power systems. The paper compares the electrical performances of two alternative reinforcement cable solutions with the base case of no reinforcement. The options of disconnecting or toggling the cables at low load as well as the automatic reactive compensation by converter voltage control are considered. Losses and voltage levels are compared for the different solutions. Investment costs and other relevant issues are discussed.

Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest

We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.

For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.

In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

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 by

K⁺ 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 < ∞