Interpolation theory in Sectorial Stieltjes Classes and Explicit System Solutions

We introduce sectorial classes of matrix-valued Stieltjes functions in which we solve the bitangential interpolation problem of Nudelman and Ball–Gohberg–Rodman. We consider also a new type of solutions of Nevanlinna–Pick interpolation problems, so-called explicit system solutions generated by Brodskii–Livsic colligations, and find conditions on interpolation data of their existence and uniqueness. We point out the connections between sectorial Stieltjes classes and sectorial operators, and find out new properties of the classical Nevanlinna–Pick interpolation matrices (in the scalar case). We present in terms of interpolation data the exact formula for the angle of sectoriality of the main operator in the explicit system solution as well as the criterion for this operator to be extremal.The interpolation model for nonselfadjoint matrices is established

Student-led podcasting for engineering education

The use of podcasts is challenging traditional communication methods in higher education, with the potential for creating highly engaging and flexible resources for learning and development. In a similar way, podcasts are helping to facilitate a stronger student identity and community within learning environments, replacing traditional student newsletter and website approaches. In this work, an innovative podcasting approach is presented in which there is a strong student-centred and student-led premise to foster and advance engineering education related uses. Podcasts are intended to cover a range of relevant engineering topics such as sharing student views on global and scientific developments, raising issues for current matters important to students and disseminating information on unique educational opportunities. Details on the set-up of the initiative are presented, and include resource requirements, management and organisation structures for an effective interface between academic staff and the student podcasting team, and mechanisms for ensuring that the podcasts maintain balanced educational outcomes

New Characterizations of Reproducing Kernel Hilbert Spaces and Applications to Metric Geometry

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

High-Temperature Interactions Between Titanium Alloys And Strontium Zirconate Refractories

We investigated interactions between Ti6Al4V alloys and strontium zirconate (SrZrO3) ceramic to assess its potential as a refractory mold material in investment casting. We developed a robust yet simple procedure to examine both the liquid–solid and solid–solid interactions using pellets in drop casting and diffusion couple methods. Reaction layers were characterized using optical microscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and x-ray diffraction (XRD). The results were compared to alumina (Al2O3) which is still a common refractory ceramic for molds in investment casting. Our findings indicate that Ti6Al4V surfaces in contact with SrZrO3 had no apparent changes in surface chemistry nor microstructure. On the other hand, Ti6Al4V surfaces in contact with Al2O3 developed γ-TiAl and α 2-Ti3Al intermetallics with thicknesses of ~ 100 μm in diffusion couples and ~ 10 μm in drop-casting experiments. Nanoindentation results showed that the surface of Ti6Al4V in contact with Al2O3 was significantly harder compared to SrZrO3, confirming our conclusion. Given the time and costs associated with mechanical and chemical removal of reaction layers on Ti6Al4V castings, SrZrO3 can be a better choice for a mold material in the investment casting of titanium alloys

Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures

A Landau-Ginsburg-Devonshire-type nonlinear phenomenological theory is presented, which enables the thermodynamic description of dense laminar polydomain states in epitaxial ferroelectric thin films. The theory explicitly takes into account the mechanical substrate effect on the polarizations and lattice strains in dissimilar elastic domains (twins). Numerical calculations are performed for PbTiO3 and BaTiO3 films grown on (001)-oriented cubic substrates. The "misfit strain-temperature" phase diagrams are developed for these films, showing stability ranges of various possible polydomain and single-domain states. Three types of polarization instabilities are revealed for polydomain epitaxial ferroelectric films, which may lead to the formation of new polydomain states forbidden in bulk crystals. The total dielectric and piezoelectric small-signal responses of polydomain films are calculated, resulting from both the volume and domain-wall contributions. For BaTiO3 films, strong dielectric anomalies are predicted at room temperature near special values of the misfit strain.Comment: 19 pages, 8 figure

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Finnish flow diverter study : 8 years of experience in the treatment of acutely ruptured intracranial aneurysms

Background Flow diversion of acutely ruptured intracranial aneurysms (IAs) is controversial due to high treatment-related complication rates and a lack of supporting evidence. We present clinical and radiological results of the largest series to date. Methods This is a nationwide retrospective study of acutely ruptured IAs treated with flow diverters (FDs). The primary outcome was the modified Rankin Scale (mRS) score at the last available follow-up time. Secondary outcomes were treatment-related complications and the aneurysm occlusion rate. Results 110 patients (64 females; mean age 55.7 years; range 12-82 years) with acutely ruptured IAs were treated with FDs between 2012 and 2020 in five centers. 70 acutely ruptured IAs (64%) were located in anterior circulation, and 47 acutely ruptured IAs (43%) were blister-like. A favorable functional outcome (mRS 0-2) was seen in 73% of patients (74/102). Treatment-related complications were seen in 45% of patients (n=49). Rebleeding was observed in 3 patients (3%). The data from radiological follow-ups were available for 80% of patients (n=88), and complete occlusion was seen in 90% of aneurysms (79/88). The data from clinical follow-ups were available for 93% of patients (n=102). The overall mortality rate was 18% (18/102). Conclusions FD treatment yields high occlusion for acutely ruptured IAs but is associated with a high risk of complications. Considering the high mortality rate of aneurysmal subarachnoid hemorrhage, the prevention of rebleeding is crucial. Thus, FD treatment may be justified as a last resort option.Peer reviewe

Finnish flow diverter study : 8 years of experience in the treatment of acutely ruptured intracranial aneurysms

Background Flow diversion of acutely ruptured intracranial aneurysms (IAs) is controversial due to high treatment-related complication rates and a lack of supporting evidence. We present clinical and radiological results of the largest series to date. Methods This is a nationwide retrospective study of acutely ruptured IAs treated with flow diverters (FDs). The primary outcome was the modified Rankin Scale (mRS) score at the last available follow-up time. Secondary outcomes were treatment-related complications and the aneurysm occlusion rate. Results 110 patients (64 females; mean age 55.7 years; range 12-82 years) with acutely ruptured IAs were treated with FDs between 2012 and 2020 in five centers. 70 acutely ruptured IAs (64%) were located in anterior circulation, and 47 acutely ruptured IAs (43%) were blister-like. A favorable functional outcome (mRS 0-2) was seen in 73% of patients (74/102). Treatment-related complications were seen in 45% of patients (n=49). Rebleeding was observed in 3 patients (3%). The data from radiological follow-ups were available for 80% of patients (n=88), and complete occlusion was seen in 90% of aneurysms (79/88). The data from clinical follow-ups were available for 93% of patients (n=102). The overall mortality rate was 18% (18/102). Conclusions FD treatment yields high occlusion for acutely ruptured IAs but is associated with a high risk of complications. Considering the high mortality rate of aneurysmal subarachnoid hemorrhage, the prevention of rebleeding is crucial. Thus, FD treatment may be justified as a last resort option.Peer reviewe