Syftet med vår studie är att bidra med kunskap om på vilket sätt speciallärare arbetar språkutvecklande med elever med speciella utbildningsbehov i matematik och som samtidigt har språkstörning. Tidigare forskning visar att språkstörning har stor inverkan på elevers kunskpasinhämtning i matematik om de samtidigt har SUM. Studien genomfördes med semistrukturerade djupintervjuer, Resultaten har bearbetats mot tidigare forskning. Vi fann att alla speciallärare vi intervjuat arbetatde på ett språkutvecklande sätt i matematikundervisningen. Trots att speciallärarna hade olika kunskap om språkstörning arbetade de alla på liknande sätt med språkutveckling i matematiken.

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Aqueous mineral oxide surfaces are ubiquitous in nature, where they play an important role in soil erosion, delta formation etc. Understanding the interfacial solvent environment at mineral oxide surfaces is important as many reactions, e.g., mineral dissolution, heterogeneous catalysis, and electrochemical water splitting occur at interfaces.Vibrational sum frequency generation (vSFG), a second-order nonlinear spectroscopic technique, inherently surface specific under the electric dipole approximation, serves as an excellent tool to study aqueous interfaces. vSFG is forbidden in centrosymmetric environments under the electric dipole approximation, making vSFG inherently specific to non-centrosymmetric environments such as surfaces, where the centrosymmetry is broken. vSFG is capable of measuring interfacial structure and dynamics without contributions from the bulk. Though vSFG has been extensively used to study aqueous interfaces yet there remain fundamental questions that need to be addressed. Is the interface capable of perturbing the environment of a centrosymmetric molecule to render it vSFG active? What higher order multipole terms contribute to vSFG? What are the vibrational energy relaxation pathways and mechanisms at oxide/water interfaces? In this dissertation, we have employed Stark active IR probe molecules (SCN-, N3-), that are sensitive to the local environment and whose frequency shifts depend on the localized electrostatic potential, to understand the interfacial solvent environment and measure the electrostatic potential associated with the charged sites at the aqueous Al2O3(0001) surface. The vibrational lifetime of IR probe molecules sheds information on solvent polarity, H-bonding network, and applied external electric fields. Hence, measuring the vibrational dynamics, whose timescales are comparable to the vibrational lifetime of the IR probe molecules, is a useful tool to understand vibrational energy relaxation (VER) pathways and mechanisms, specific solute-solvent interactions, and localized solvent environment. Though IR probe molecules have been employed to study bulk solvents, the literature for interfaces/surfaces is limited to reverse micelles, air/water interfaces and metal electrode surfaces. The VER rates of IR probe molecules (charged solutes) in bulk solvent and confined solvent environments are significantly different, which reflects the different local properties. The aim of this dissertation is to understand the localized solvent environment as well as the VER pathways and mechanisms of the IR probe molecule (SCN-) at the aqueous mineral oxide interfaces using IR pump-vSFG probe spectroscopy. Bulk H2O and D2O are similar in terms of H-bonding capability, static dielectric constant, and dipole moment. The FTIR spectra of the CN stretch of SCN- in bulk H2O and D2O share a similar central frequency, yet the measured vibrational lifetimes of SCN- reveal accelerated vibrational energy relaxation in bulk H2O vs. bulk D2O, indicating fundamental differences between the two solvent environments. This reflects distinct vibrational energy relaxation pathways. Probing the vibrational lifetime of the CN stretch of SCN- at the alumina(0001)/H2O and alumina(0001)/D2O interfaces enabled us to understand the effect of the interfacial solvent density of states on the solute-solvent vibrational coupling at interfaces. We observed three times faster vibrational energy relaxation (VER) for interfacial D2O (T1 ~7 ps) compared to bulk D2O (T1 ~22 ps). The lifetime of the CN stretch at the α-Al2O3(0001)/H2O interface (T1 ~3 ps) is, however, similar to the dynamics in bulk H2O (T1 ~ 2.7 ps) where effective coupling with the solvent combination band (water bending + librational modes) provides an efficient pathway for intermolecular vibrational energy transfer. Ab-initio simulations show that there is an increase in the vibrational density of states (VDOS) at the interface in the low-frequency region of the O-D stretch, resulting in greater overlap between SCN- and D2O vibrational modes compared to the bulk D2O. The VDOS is not the only factor determining VER. At the interface, there are likely enhanced solute-solvent interactions due to increased transition dipole – transition dipole coupling, as a result of reduced dielectric constant and more net oriented molecules. The two factors (a) availability of accessible energy-accepting states of the solvent and (b) increased solute-solvent coupling, cause acceleration in the vibrational relaxation at the alumina/D2O interface. This work provides insight into the vibrational relaxation pathways and coupling between solute and solvent vibrational modes, which is essential for understanding fundamental condensed phase phenomena in the bulk as well as at interfaces. Our research suggests that VER dynamics cannot be generalized for all interfaces as there are significant differences between how charged solutes behave within confined reverse micelles, at the air/water interface, and at solid/water interfaces. In this dissertation, the basic question of the origin of non-centrosymmetry is also addressed by studying the steady state vSFG response from the azido stretch of N3-, a centrosymmetric molecule, at the α-Al2O3 (0001)/H2O interface. We observed the azide asymmetric stretch peak at the aqueous alumina interface demonstrating that the interface sufficiently perturbs the centrosymmetric environment of the azide ion to make it vSFG active, thereby re-emphasizing the surface-specificity of the vSFG technique. DFT calculations revealed that the application of an external electric field (in the range 0.1 - 0.5 V/Å, similar to the ones typically observed at interfaces), 1-3 the centrosymmetry of the azide ion is broken, introducing Raman activity to the previously IR only active mode (asymmetry azide stretch) thereby making the mode vSFG active. Unlike metal surfaces, where the electrostatic potential is homogeneously distributed over the surface, mineral oxide surfaces have localized and spatially heterogeneous charged sites depending on the bulk pH solution, due to protonation/deprotonation of terminal hydroxyl groups. We employed the asymmetric stretching frequency of N3, an IR probe molecule, that is sensitive to the local solvent environment and applied electric potential to determine the localized interfacial electrostatic potential. Having demonstrated that the interface perturbs the centrosymmetry of N3-, shifts in the central frequency of its asymmetric stretch mode can be used to report on the interfacial localized surface potential of the Al2O3 surfaces. Our previous work using Stark active SCN- to probe the localized charged sites of the alumina (0001)/H2O interface led to the foundation of vSFG spectroscopy as a probe of the local electrostatic potential. Using the N3- Stark tuning rate, the localized electrostatic potential at the negatively charged Al-O- sites was measured to be -170 mV, similar to the one measured by SCN- (-154 mV). In this dissertation, we expand the library of nitrile groups that can be used to measure the interfacial electrostatic potential by using N3-, another Stark active IR molecule, while probing the origin of non-centrosymmetry in this centrosymmetric molecule at mineral oxide/water interfaces. / Chemistry

Channel coding plays a vital role in telecommunication. Low-Density Parity- Check (LDPC) codes are linear error-correcting codes. According to the 3rd Generation Partnership Project (3GPP) TS 38.212, LDPC is recommended for the Fifth-generation (5G) New Radio (NR) shared channels due to its high throughput, low latency, low decoding complexity and rate compatibility. LDPC encoding chain has been defined in 3GPP TS 38.212, but some details of LDPC encoding chain are still required to be explored in the MATLAB environment. For example, how to deal with the filler bits for encoding and decoding. However, as the reverse process of LDPC encoding, there is no information on LDPC decoding process for 5G NR shared channels in 3GPP TS 38.212. In this thesis project, LDPC encoding and decoding chains were thoughtfully developed with MATLAB programming based on 3GPP TS 38.212. Several LDPC decoding algorithms were implemented and optimized. The performance of LDPC algorithms was evaluated using block error rate (BLER) v.s. signal to noise ratio (SNR) and CPU time. Results show that the double diagonal structure-based encoding method is an efficient LDPC encoding algorithm for 5G NR. Layered Sum Product Algorithm (LSPA) and Layered Min-Sum Algorithm (LMSA) are more efficient than Sum Product Algorithm (SPA) and Min-Sum Algorithm (MSA). Layered Normalized Min-Sum Algorithm (LNMSA) with proper normalization factor and Layered Offset Min-Sum Algorithm (LOMSA) with good offset factor can optimize LMSA. The performance of LNMSA and LOMSA decoding depends more on code rate than transport block. / Kanalkodning spelar en viktig roll i telekommunikation. Paritetskontrollkoder med låg densitet (LDPC) är linjära felkorrigeringskoder. Enligt tredje generationens partnerskapsprojekt (3GPP) TS 38.212, LDPC rekommenderas för den femte generationens (5G) nya radio (NR) delade kanal på grund av dess höga genomströmning, låga latens, låga avkodningskomplexitet och hastighetskompatibilitet. LDPC kodningskedjan har definierats i 3GPP TS 38.212, men vissa detaljer i LDPC kodningskedjan krävs fortfarande för att utforskas i Matlabmiljön. Till exempel hur man hanterar fyllnadsbitar för kodning och avkodning. Men som den omvända processen för LDPC kodning finns det ingen information om LDPC avkodningsprocessen för 5G NR delade kanaler på 3GPP TS 38.212. I detta avhandlingsprojekt utvecklades LDPC-kodning och avkodningskedjor enligt 3GPP TS 38.212. Flera LDPC-avkodningsalgoritmer implementerades och optimerades. Prestandan för LDPC-algoritmer utvärderades med användning av blockfelshalt (BLER) v.s. signal / brusförhållande (SNR) och CPU-tid. Resultaten visar att den dubbla diagonala strukturbaserade kodningsmetoden är en effektiv LDPC kodningsalgoritm för 5G NR. Layered Sum Product Algorithm (LSPA) och Layered Min-Sum Algorithm (LMSA) är effektivare än Sum Product Algorithm (SPA) och Min-Sum Algorithm (MSA). Layered Normalized Min-Sum Algorithm (LNMSA) med rätt normaliseringsfaktor och Layered Offset Min-Sum Algorithm (LOMSA) med bra offsetfaktor kan optimera LMSA. Prestandan för LNMSA- och LOMSA-avkodning beror mer på kodhastighet än transportblock.

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