In an earlier paper, we described bordered algebras for knot Floer homology. In this paper, we introduce a differential graded algebra, the pong algebra and compute the A-infinity structure on its homology.

We explain how to use bordered algebras to compute a version of link Floer homology. As a corollary, we also give a fast computation of the Thuston polytope for links in the three-sphere.

The generalized operator-based Prony method is an important tool for describing signals which can be written as finite linear combinations of eigenfunctions of certain linear operators. On the other hand, Bernoulli's algorithm and its generalizations can be used to recover the parameters of rational functions belonging to finite-dimensional subspaces of $H_2$ Hardy-Hilbert spaces. In this work, we discuss several results related to these methods. We discuss a rational variant of the generalized operator-based Prony method and show that in fact, any Prony problem can be treated this way. This realization establishes the connection between Prony and Bernoulli methods and allows us to address some well-known numerical pitfalls. Several numerical experiments are provided to showcase the usefulness of the introduced methods. These include problems related to the identification of time-delayed linear systems and parameter recovery problems in reproducing kernel Hilbert spaces.

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups.

The paper presents a novel control strategy for autonomous vehicles, which can effectively handle the nonlinear effects and uncertainties of the controlled system. This solution is based on a new formulation of the ultra-local model-based control approach. This method can deal with the unknown dynamics and other uncertainties of the vehicle without any further measurement or complex modelling process. The control methods require a reduced-complexity nominal linear model of the system, and the unknown part is continuously estimated by the proposed ultra-local model. The proposed control-oriented vehicle modelling method leads to an increased performance level of vehicle motion. The effectiveness of the proposed method through a high-fidelity vehicle simulator (CarMaker) is illustrated. Moreover, the operation of the control through its implementation on a test vehicle of ThyssenKrupp is also demonstrated.

A wide class of nonlinear systems can be described by functional series representations like Volterra- and Fliess - series. It is a known result that Volterra – series approximators as finite dimensional models for nonlinear systems can be constructed as nonlinear moving average (NLMA) operators cascaded with static polynomial nonlinearities. This motivates the use of block – oriented modeling and control of certain nonlinear systems. This talk will discuss the modeling and identification issues of frequently used block oriented (Wiener – Hammerstein) and bilinear models and some related problem like dynamic inversion and unknown input estimation. Embedding nonlinear models into linear ones (immersion) will be considered, too. An application for obtaining yaw – dynamic models for self a driving car operating at various speeds will be shown for illustration.

Atomic layer deposition was used to grow epitaxial iron sulfide layers on alpha-Al2O3 substrates. According to the transmission electron microscopic measurements, these Fe-sulfide films had 1C pyrrhotite structure (Fe1-xS). In the case of pyrrhotite materials, both the magnetic and electric properties depend significantly on their iron content and on the ordering of iron vacancies. By tuning the parameters of the atomic layer deposition method, the structure of epitaxial pyrrhotite films could be controlled, thus the electronic properties of the Fe1-xS films could be influenced: At deposition temperatures below 350 degrees C, the structure contained many faults, and the layers were n type semiconductors, while at higher temperatures, the resulting films were p-type with excellent crystalline structures with disordered vacancies. A post deposition annealing could further improve the crystallinity and induce p-type conductivity.

In this paper we study smooth structures on closed oriented 4-manifolds with fundamental group Z_2 and definite intersection form. We construct infinitely many irreducible, smooth, oriented, closed, definite four-manifolds with fundamental group Z_2 and second Betti number 1 and 2. As an application, we prove that when the second Betti number of a definite four-manifold with fundamental group Z_2 is positive and it admits a smooth structure, then it admits infinitely many smooth structures.

We study the minimal genus problem for some smooth four-manifolds.

The present work explores the atomic layer deposition (ALD) of VO2 layers for resistive switching applications. Tetrakis (ethylmethylamino)vanadium (TEMAV) precursor was used combined with different oxidants, deposition temperatures, and annealing procedures, and the structural and electrical properties of the layers were analysed. All the as-deposited layers were amorphous, but an annealing in oxygen containing atmosphere at temperatures exceeding 400 degrees C yielded pure and crystalline VO2 layers. The thus prepared films are compact with crystallite sizes between 50 and 100 nm, displaying excellent electrical switching properties, with their resistivity decreasing 3 orders of magnitude at 68 degrees C.

In an earlier paper, we introduced ``bordered knot algebras'', which are graded algebras indexed by a pair of integers (m,k). In a subsequent paper, we introduced a two-parameter family of differential graded algebra, the ``pong algebras'', and identified their homology with the bordered knot algebras, and characterized the induced A-infinity structure on the homology. The aim of the present paper is to give an explicit, combinatorial model for this A-infinity structure on the bordered knot algebras, and a further weighted deformation of this structure, in the case where k=1.

Inspired by a recent result of Levine-Lidman-Piccirillo, we construct infinitely many exotic smooth structures on some closed four-manifolds with definite intersection form and fundamental group isomorphic to $\Z /2\Z$. Similar constructions provide exotic smooth structures on further four-manifolds with fundamental group $Z/2\Z$, including examples with even $b_2^+$.

Using elliptic fibrations with specific singular fibers, we find spheres with very negative self-intersections in elliptic surfaces and in their blow-ups.

Two methods were proposed and implemented for the fabrication of channel waveguides in an Er-doped Tellurite glass. In the first method, channel waveguides were fabricated by implanting 1.5 MeV and 3.5 MeV energy N+ ions through a special silicon mask to the glass sample at various fluences. Those waveguides implanted at a fluence of 1.0 × 1016 ions/cm2 operated up to 980 nm, and showed green upconversion of the Erbium ions. In the second method, channel waveguides were directly written in the Er3+: TeO2W2O3 glass using an 11 MeV C4+ ion microbeam with fluences in the range of 1 · 1014–5 · 1016 ions/cm2. The waveguides worked in single mode regime up to the 1540 nm telecom wavelength. Propagation losses were reduced from the 14 dB/cm of the as-irradiated waveguides by stepwise thermal annealing to 1.5 dB/cm at λ = 1400 nm.

Model Free Control (MFC) with ultra-local model is novel design method to provide high performance control for systems with nonlinear dynamics. The basic concept of this approach is to compute an ultra-local model, which is valid for a short period of time. Although the concept has already been successfully applied for various vehicle control problems, there are some open issues regarding the robustness and the stability of the closed-loop controlled system. This paper presents a method for designing a robust control based on $\mathcal{H}_{\infty}$ synthesis, with which a solution on these issues can be found. In the proposed MFC strategy the ultra-local model-based control is in the inner loop of the control structure. Moreover, a robust $\mathcal{H}_{\infty}$ control for the outer loop is designed, in whose control-oriented model the control of the inner loop is incorporated. The control strategy is implemented in high-fidelity vehicle dynamic environment and its efficiency and operation are demonstrated through a complex simulation example.

Demographic transformation, characterized by the aging of the population, is causing an increasing problem in developed countries. This change involves a significant increase in the number of chronic diseases, the health damage generated by which causes loss of life years due to deteriorating health and impairs quality of life. Among chronic diseases, the increasing frequency of musculoskeletal disorders has become characteristic of an aging society, which causes the greatest loss of life years in Hungary due to limitations. These problems mean increasing social, economic, and administrative pressure on the population and pose solution challenges for the spa town leaders and health decision-makers. There are several therapies available in the medical and health sciences to prevent and treat musculoskeletal disorders, with increasing emphasis on conservative therapies as the role of health increases. In Hungary, among these procedures, medicinal water treatment services based on natural healing factors available in spa towns play a key role, which is also the basis of medical tourism and part of the health care system. To solve the problems caused by musculoskeletal disorders, it is essential to know the occurrence of the disease and the treatment-use attitude of the patients, mainly due to the COVID-19 pandemic. Therefore, the main goal of our research is to assist spa towns leaders and health decision-makers in the implementation of medical tourism developments and more optimal patient care. One of the part-aims of our research is to reveal the regional differences of the most common musculoskeletal diseases in Hungary based on secondary data. Our other research-part objective is to determine the impact of socio-demographic characteristics, health status, type of musculoskeletal disease, pain, and commitment to bath medicine care system on the future use of medicinal water treatment in patients with musculoskeletal disorders. Based on our results, we declare that the health status of the Hungarian population in terms of the most frequently occurring locomotor diseases is worst in Central Hungary, the greater part of the Southern Great Plain, and the northeastern part of the country. In terms of territory, we concluded that the incidence of musculoskeletal disorders is relatively low, and moderate inequality in Hungary. It also follows from our results that the indicators measuring regional differences selected can be successfully applied to examine the territorial inequalities of musculoskeletal diseases concerning medical tourism. We also found that the respondents' level of family income, place of residence by region, state of health, the degree of commitment to medicinal water treatment/service was found, furthermore the cost of treatment, and the cost of accommodation /travel, significantly affect the planned use of the medicinal water treatment in the future. Our results promote the implementation of more targeted medical tourism and health industry developments in spa towns.

We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We prove an inequality between \beta (K) and the (knot Floer) thickness of K. As an application we show that all Montesinos knots have thickness at most one.

The aim of this paper is to identify the pong algebra defined in our earlier work with a certain endomorphism algebra in the wrapped Fukaya category of the symmetric product of a disk.

We introduce a numerical invariant β( K ) ∈ (cid:78) ∪ { 0 } of a knot K ⊂ S 3 which measures how nonalternating K is. We prove an inequality between β( K ) and the (knot Floer) thickness th ( K ) of a knot K . As an application we show that all Montesinos knots have thickness at most one.