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In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: The key tools behind our results are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier transforms for functions such that their Fourier transforms are of monotone type or lacunary series.

Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A decomposition space We establish readily verifiable criteria which ensure the existence of a continuous inclusion (“an embedding”) In a nutshell, in order to apply the embedding results presented in this article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings. These sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of We also prove a The resulting embedding theory is illustrated by applications to

In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér Interpolation Problem for matrix rational functions. We then extend the

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this present paper we consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain We also study in detail the mother body problem associated to To construct the mother body measure, we define a quadratic differential Following previous works of Bleher & Kuijlaars and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials. Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of the associated

This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways.Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool.This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.

The Mediterranean Sea is considered a hot spot of global warming because it has been changing faster than the global ocean, creating a strong impact on the marine environment. Recent studies agree on the increase in the sea level, in the sea surface temperature, and in the sea surface salinity in the Mediterranean Sea over the last two decades. In this research, the possible interconnection between these and other parameters that contribute to the regulatory effect of the sea on the climate are identified and discussed. Spatio-temporal variability of four oceanographic and air–sea interaction parameters (sea-level, sea surface temperature, sea surface salinity, and freshwater flux) are estimated over the last 27 years by performing the empirical orthogonal function analysis. Climatic trends, and interannual and decadal variability of the different datasets are delineated and described in the whole Mediterranean and in its sub-basins. On the climatic scale, the Mediterranean and its sub-basins behave in a coherent way, showing the seal level, temperature, salinity, and freshwater flux rise. On the interannual scale, the temporal evolution of the sea level and sea surface temperature are highly correlated, whereas freshwater flux affects the variability of sea level, temperature, and the salinity field mainly in the Western and Central Mediterranean. The decadal signal associated with the Northern Ionian Gyre circulation reversals is clearly identified in three of the four parameters considered, with different intensities and geographical extents. This signal also affects the intermediate layer of the Eastern Mediterranean, from where it is advected to the other sub-basins. Decadal signal not associated with the Northern Ionian Gyre reversals is strongly related to the variability of main sub-basin scale local structures.

Ocean swell activities excite body‐wave microseisms that contain information on the Earth's internal structure. Although seismic interferometry is feasible for exploring structures, it faces the problem of spurious phases stemming from an inhomogeneous source distribution. This paper proposes a new method for inferring seismic discontinuity structures beneath receivers using body‐wave microseisms. This method considers the excitation sources of body‐wave microseisms to be spatially localized and persistent over time. To detect the P‐s conversion beneath the receivers, we generalize the receiver function analysis for earthquakes to body‐wave microseisms. The resultant receiver functions are migrated to the depth section. The detected 410‐ and 660‐km mantle discontinuities are consistent with the results obtained using earthquakes, thereby demonstrating the feasibility of our method for exploring deep‐earth interiors. This study is a significant step toward body‐wave exploration considering the sources of P‐wave microseisms to be isolated events. Plain Language Summary The ocean waves excite persistent and random ground motions called microseisms. Since this excitation is independent of seismic activities, this wavefield has information about seismic structures that earthquakes never have. For the deep structure, such as the mantle and core, body‐wave microseisms are more suitable than surface‐wave microseisms because body‐wave microseisms have better sensitivity. Previous studies using body‐wave microseisms mainly adopted the cross‐correlation analysis known as seismic interferometry. This method assumes that the microseisms are excited everywhere. However, the inhomogeneous source distribution of body‐wave microseisms causes artifacts for exploration by seismic interferometry. We developed a new method which circumvents this problem. Assuming that the body‐wave microseisms are spatially isolated, this method extracted the P‐s converted waves beneath receivers from body‐wave microseisms. The 3‐Dimensional imaging result of extracted P‐s converted waves shows both 410‐ and 660‐km mantle discontinuities, consistent with results using earthquakes. This study shows the potential of body‐wave microseisms for exploring the deep earth structure. Key Points The P‐S waves at mantle discontinuities were extracted from the ambient noise excited by the ocean swells We developed the source deconvolution method to generalize a receiver function method to P‐wave microseisms The migration result of P‐S waves was consistent with previous studies, showing the potential of P‐wave microseisms to seismic structures

Woody plants play a vital role in global ecosystems and serve as valuable resources for various industries and human needs. While many woody plant genomes have been fully sequenced, gene function research and biotechnological breeding advances have lagged behind. As a result, only a limited number of genes have been elucidated, making it difficult to use newer tools such as CRISPR-Cas9 for biotechnological breeding purposes. The use of Agrobacterium rhizogenes as a transformative tool in plant biotechnology has received considerable attention in recent years, particularly in the research field on woody plants. Over the past three decades, numerous woody plants have been effectively transformed using A. rhizogenes -mediated techniques. Some of these transformed plants have successfully regenerated. Recent research on A. rhizogenes -mediated transformation of woody plants has demonstrated its potential for various applications, including gene function analysis, gene expression profiling, gene interaction studies, and gene regulation analysis. The introduction of the Ri plasmid has resulted in the emergence of several Ri phenotypes, such as compact plant types, which can be exploited for Ri breeding purposes. This review paper presents recent advances in A. rhizogenes-mediated basic research and Ri breeding in woody plants. This study highlights various aspects of A. rhizogenes-mediated transformation, its multiple applications in gene function analysis, and the potential of Ri lines as valuable breeding materials

Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let In another article to appear, we will prove that when

In the manufacturing of composite materials, achieving high precision in drilling processes is crucial to ensure product quality and performance. This study investigates the influence of drilling parameters on key performance metrics delamination, circularity, and cylindricity using the Taguchi method. An L25 orthogonal array was employed to systematically explore the effects of spindle speed, feed, and drill type on the quality of drilled holes. The analysis of variance (ANOVA) revealed that feed significantly influences the outcomes across all drill materials, with cutting speed playing a secondary role. The study further applied desirability function analysis (DFA) to optimize these multi-responses, identifying the optimal parameter settings for each drill type. The results highlight the critical role of feed in minimizing delamination, circularity, and cylindricity with the optimal settings offering significant improvements in drilling performance.