A general method for calculating mass and stiffness matrices of H (curl)-conforming finite elements is proposed. It applies to curvilinear geometries and/or inhomogeneous materials, preserves the nullspace of the curl operator, and is computationally efficient. In the finite element integrals, the terms incorporating the effects of geometry and materials are expanded in a series of multivariate polynomials. As a result, the element matrices can always be integrated analytically by means of predefined universal matrices. The mapping from the reference element to the physical configuration is done by suitable forms of the Piola transformation so that the resulting finite element bases are guaranteed to preserve the nullspace of the curl operator. A mathematical proof, including the curvilinear case, is included. The suggested approach features a representation limit: When the metric expansion is continued beyond a critical order, which is determined by the order of the finite element basis, the truncation error becomes zero. Hence, the number of universal matrices is bounded, and the sole source of error is the numerical calculation of the expansion coefficients for the metric terms. The method is validated by numerical examples, and its computational efficiency is demonstrated by a comparison to competing approaches.

The finite element method (FEM) has benefited recently from the introduction of the domain decomposition method (DDM), especially to tackle large-scale problems.Many versions of DDM may be found in the literature, and almost none of them have used a rigorous approach to show the accuracy of the formulation.Here, we suggest the use of the method of manufactured solutions (MMS) to introduce DDM into a FEM code.This approach also allows us to debug the demanding coding process of the method.First, we introduce the mandatory operators used for DDM to construct second-order absorbing boundary conditions.Then, we use these results to show the correct implementation of DDM with basis functions up to fourth order for tetrahedra, triangular prisms, and hexahedra, obtaining the convergence rates predicted by the classic FEM theory.Finally, we illustrate how to use MMS to test different formulations, assessing the effect of using different spaces and orders for the arising ancillary variables.

A compact wide-acceptance angle (around +/- 50 degrees) high-energy-resolution 2D electron analyzer CoDELMA (Compact DELMA) is proposed, constructed and tested. CoDELMA is composed of a recently-proposed variable -deceleration-ratio wide-acceptance-angle electrostatic lens (VD-WAAEL), a cylindrical mirror analyzer (CMA) and a projection lens. After a brief review of VD-WAAEL, the use of a plane grid in the lens is presented as a new design option, which allows keeping the focusing angle almost constant irrespective of the deceleration ratio. A detailed consideration is given to the combination of CMA and a projection lens, which allows simultaneous analysis of wide reciprocal ( +/- 8 degrees) and real space ( +/- 5 mm) at the entrance of CMA. CoDELMA is the successor to the previously developed DELMA instrument including a concentric hemispherical analyzer. The whole system of CoDELMA becomes much more compact than that of DELMA owing to the use of VD-WAAEL and CMA, and this results in considerable reduction of the production cost. Results of test measurement of energy spectrum and angular distribution using an electron gun as an excitation source confirmed that the energy resolution and the acceptance angle are almost the same as the designed values.

A new $H^{1}$-conforming finite-element basis is proposed. The basis functions are hierarchical in terms of the polynomial order and feature symmetries in terms of barycentric coordinates. The corresponding element matrices exhibit high levels of sparsity and moderate condition numbers in the higher-order case. Moreover, the basis functions are pairwise orthogonal with respect to the finite-element interpolation operator, which is given in explicit form. Thus, the basis possesses not only hierarchical but also interpolatory properties. The resulting interpolation scheme is efficient because it requires the evaluation of only a single scalar product per basis function. An example is presented, where the proposed interpolation scheme is used to construct inhomogeneous Dirichlet boundary conditions. The numerical results confirm that interpolation yields the same asyptotic rate of convergence as $L^{2}$ approximation, which is much more expensive.

The contents of this repository are associated with the paper: [1] L. L. Toth, A. Amor-Martin, and R. Dyczij-Edlinger, "Hierarchical Universal Matrices for Curvilinear Tetrahedral H(curl) Finite Elements," submitted to IEEE Transactions on Antennas and Propagation. The subdirectory UniversalMatrices contains mathematical formulas for hierarchical L2 and H(curl) basis functions, the corresponding universal matrices (UM), and a MATLAB script for generating these UMs. The bases and UMs are given in two different formats: *.mat MATLAB data file with a MATLAB structure, *.xml file with a structure. The subdirectory MATLAB_TestCode contains MATLAB scripts and input data for reproducing the numerical results given in [1]. For details, see the README.txt files in the bottom-level directories.

The front cover illustrates the diastereoselective formation of condensed heterocyclic ring systems by domino reaction sequences. The dominoes toppling each other represent the steps of the reaction sequences, each transformation initiating the next one. The mechanism of the cyclization is tunable by the choice of reagent, affording four different condensed heterocyclic ring systems. A novel mild transformation of nitroarenes to N-hydroxyindoles, in which deoxygenation is carried out by an intramolecular nitro-Diels-Alder cyclization-ring opening, is presented. Details can be found in the Research Article by Attila Mándi, Tibor Kurtán, and co-workers (S. B. Király, L. Tóth, T. Kovács, A. Bényei, E. Lisztes, B. I. Tóth, T. Bíró, A. Kiss-Szikszai, K. E. Kövér, A. Mándi, T. Kurtán, Adv. Synth. Catal. 2023, 365, XXXX–XXXX; DOI: 10.1002/adsc.202300083)

Domino Knoevenagel-cyclization reactions of 2H-chromene and chroman derivatives containing o-formylaryl amine or ether side-chain was carried out to produce four series of chiral condensed heterocycles representing four novel skeletons and exhibiting antiproliferative activity. The cyclization step occurred with four different mechanisms: a concerted intramolecular hetero Diels-Alder reaction (IMHDA), a stepwise polar [2+2] cycloaddition, a [1,5]-hydride shift-6-endo cyclization or a multi-step nitro hetero Diels-Alder-ring-opening-Cadogan-type cyclization sequence. The latter reaction provided a new route to hydroxyindoles by an inverse Cadogan-type cyclization, in which the nitro group is deoxygenated by a nitro IMHDA-ring-opening sequence. The cyclization mechanisms and their stereoselectivity were studied by DFT calculations, based on which we proposed a mechanism for the multi-step cyclization to hydroxyindoles and explained the observed diastereoselectivity.

A time-domain state-space solver based on weighted Laguerre polynomials is presented. It is specifically designed for the design optimization of structures excited by predefined pulses. Applications include time-domain reflectometry, radar, and sonar. Such settings have in common that large numbers of systems are to be analyzed for the same excitation. The proposed method features offline-online decomposition, computes the Laguerre expansion of the system response at low cost, and facilitates its transformation to the frequency-domain. The algorithm is validated by a numerical example, involving dispersive material properties. Its performance is compared to that of a Runge-Kutta time-stepping method, with a focus on multi-query settings. A numerical example shows that the computation time of the new method is significantly faster than the Runge-Kutta method.

A new serendipity function space for hexahedral H(curl)-conforming finite-elements, called the mixed-order serendipity space, was recently introduced by the authors. Its key feature is its hierarchical basis. Moreover, the number of basis functions and, consequently, the number of unknowns is significantly less than for the mixed-order Nédélec and tensor product spaces, while the convergence rates are the same. Classical hexahedral finite-element methods may experience a degradation of convergence when meshes of non-parallelpipedal or curvilinear elements are refined. This work presents a numerical convergences study for several H(curl) conforming finite-element bases in the curvilinear case. It is shown that a special, yet versatile, refinement method, called quasi-affine refinement, can restore the optimal rate of convergence in all cases. Amongst the considered finite-element spaces, the mixed-order serendipity spaces require the smallest number of unknowns.

A paksi telephelyen tervezett új atomerőműblokkok szükségessé tették a terület szeizmicitásának és földrengés-veszélyeztetettségének felülvizsgálatát, a húsz-huszonöt éve készült és az akkori elképzeléseket, tudást és adatokat tükröző földrengésveszély-elemzés megújítását

A new serendipity function space for hexahedral H(curl)-conforming finite elements, the so-called mixed-order serendipity space, is proposed. In the case of arbitrary parallelepiped meshes, the resulting asymptotic rate of convergence of the H(curl)-norm error is exponential in the base of the mesh size and in terms of the finite element order. Compared to tensor product spaces, the number of unknowns is much smaller, whereas the rate of convergence remains the same. While the proposed serendipity space is not suitable for elements of general shape, it allows the construction of hierarchical basis functions that are compatible with some of the costly but versatile tensor product spaces. This property permits mixing different finite element spaces within one mesh, without affecting conformity.For the general curvilinear case, this paper introduces an iso-serendipity finite element for curvilinear hexahedra, which employs the proposed serendipity space and basis for representing the fields and H1 serendipity basis for representing the geometry. As the main contribution, this element achieves the same convergence rate for both curvilinear and parallelepiped meshes, by means of a special yet simple mesh refinement technique. In contrast to isogeometric methods, it only requires certain interpolation points on curvilinear boundaries rather than the entire geometry mapping. All results are supported by mathematical proofs and validated experimentally via numerical examples.

Permanent ground displacements/deformations caused by earthquakes can seriously challenge the safety of the nuclear power plants. The state-of-the-art hazard analysis methods provide a fault displacement hazard curve, i.e., the annual probability of given measure of displacement will be exceeded. The evaluation of ground displacement hazard requires great effort, empirical evidence, and sufficient data for the characterization of the fault activity and capability to cause permanent surface displacement. There are practical cases when the fault at the site area revealed to be active, and, despite this, there are no sufficient data for the evaluation of permanent ground displacements hazard and for judging on the safety significance of permanent ground displacement. For these cases, a methodology is proposed that is based on the seismotectonic modelling and results of the probabilistic seismic hazard analysis. The method provides conservative assessment of the annual probability of fault displacement that allows the decision whether permanent displacement hazard is relevant to nuclear power plant safety. The feasibility and applicability of the method is demonstrated for the Paks site, Hungary.

Domino cyclization reactions of N-aryl-1,4- and 1,5-benzoxazepine derivatives involving [1,5]-hydride shift or C(sp2)-H functionalization were investigated. Neuroprotective and acetylcholinesterase activities of the products were studied. Domino Knoevenagel-[1,5]-hydride shift-cyclization reaction of N-aryl-1,4-benzoxazepine derivatives with 1,3-dicarbonyl reagents having active methylene group afforded the 1,2,8,9-tetrahydro-7bH-quinolino [1,2-d][1,4]benzoxazepine scaffold with different substitution pattern. The C(sp3)-H activation step of the tertiary amine moiety occurred with complete regioselectivity and the 6-endo cyclization took place in a complete diastereoselective manner. In two cases, the enantiomers of the chiral condensed new 1,4-benzoxazepine systems were separated by chiral HPLC, HPLC-ECD spectra were recorded, and absolute configurations were determined by time-dependent density functional theory- electronic circular dichroism (TDDFT-ECD) calculations. In contrast, the analogue reaction of the regioisomeric N-aryl-1,5-benzoxazepine derivative did not follow the above mechanism but instead the Knoevenagel intermediate reacted in an SEAr reaction [C(sp2)-H functionalization] resulting in a condensed acridane derivative. The AChE inhibitory assays of the new derivatives revealed that the acridane derivative had a 6.98 μM IC50 value.

The seismicity of Hungary can be considered moderately active, nevertheless contemporary reports from the past approx. 350 years documented surface manifestations of liquefaction occurrences. The last such earthquake was the 1956 Dunaharaszti ground motion, for which the location of two liquefied sites could be identified approx. 60 years after the event. This provided an excellent opportunity to analyze possibly the only accessible liquefied sites in Hungary. Analysis of the two sites included field and laboratory tests allowing the back-calculation of maximum horizontal ground acceleration of the earthquake. This parameter was previously unknown because the closest seismometer saturated during the event. The performed back-analysis using the principles of paleoliquefaction studies was the first of such analyses in the country. In areas with low to moderate seismicity, geotechnical engineers often neglect and overlook liquefaction hazard, however, when it is addressed, the hazard is often overestimated due to improper characterization of the seismic loading and site characterization. To explore this observation more deeply, probabilistic seismic and liquefaction hazard assessment were carried out at the two liquefied sites and it was found that this conclusion is also valid for Hungary, but the degree of conservatism of the pseudo-probabilistic procedures decreases with increasing earthquake return period (lower annual probability of occurrence).

For the new nuclear power plants, the hazard of liquefaction due to earthquakes should be excluded by appropriate site selection or eliminated by engineering measures. An important question is how to define a quantitative criterion for negligibility of the liquefaction hazard. In the case of operating plants, liquefaction can be revealed as a beyond-design-basis event. It is important to learn whether the liquefaction hazard has a safety relevance and whether there is a sufficient margin to the onset of liquefaction. The use of pseudoprobabilistic method would be practicable for the definition of probability of liquefaction, but it could result in overconservative results. In this paper, the applicability of the pseudoprobabilistic procedure is demonstrated for the sites in diffuse seismicity environment and for low hazard levels that are typical for nuclear safety considerations. Use of the procedure is demonstrated in a case study with realistic site-plant parameters.

A new method for calculating the geometric sensitivities of curvilinear finite elements is presented. Approximating the relevant metric tensors by hierarchical orthogonal polynomials enables the sensitivity matrices to be integrated analytically. The resulting numerical method is based on pre-calculated universal matrices and achieves significant savings in computer runtime over conventional techniques based on numerical integration. Moreover, there exists a representation limit for the geometry, i.e., the degree of basis functions fully determines a critical order of the geometry expansion, beyond which the derivatives of the finite-element matrices will remain constant. To validate the suggested approach, a numerical example is presented.

Ethyl-3-formyl-6-methoxy-(2H)-chromene-2-carboxylate was transformed to N-substituted 1,2-dihydrochromeno[2,3-c]pyrrol-3-ones in a domino reductive amination–lactamization reaction. Isomerization of the double bond and the inherently labile stereogenic center was studied, and HPLC-ECD analysis of a chiral 1,2-dihydrochromeno[2,3-c]pyrrol-3(3aH)-one derivative aided by TDDFT-ECD calculation allowed configurational assignment of the separated enantiomers. Antiproliferative activity of the products was demonstrated on the CaCo-2 human epithelial colorectal adenocarcinoma cell line.

Synthesis of racemic hexahydropyrrolo[1,2-a]quinoline derivatives (1-8) was performed by utilizing the Knoevenagel-[1,5]-hydride shift-cyclization domino reaction. Separation of the enantiomers of the chiral products (1-8) was carried out by chiral high-performance liquid chromatography, and online high-performance liquid chromatography-electronic circular dichroism (ECD) spectra were recorded to elucidate the absolute configuration by comparing the experimental and time-dependent density functional theory-ECD spectra obtained at various theoretical levels. For 1 of the products, the time-dependent density functional theory-ECD calculations allowed determining both the relative and the absolute configuration by distinguishing the 4 stereoisomers. One of the compounds with spiro 1,3-cyclohexanedione moiety (7) possessed moderate acetylcholinesterase inhibitory activity, while 3 showed neuroprotective activity in oxygen-glucose deprivation-induced neurotoxicity in human neuroblastoma SH-SY5Y cells.