Weak type (1,1) bounds for singular integrals with rough kernels on block spaces

Incremental Direct Cost of Chronic Obstructive Pulmonary Disease in Colombia Using Doubly Robust Methods on Administrative Data.

Near-infrared (NIR) variability studies of active galactic nuclei (AGNs) are still limited, as long-term multiepoch monitoring in the NIR is observationally challenging. The depth, wavelength coverage, and 14-year temporal baseline of UltraVISTA make it one of the few surveys capable of providing a detailed characterization of AGN variability in this regime. We aim to quantify the NIR variability of known AGNs in the COSMOS field and to investigate the physical origin of variability in type 2 AGNs. In particular, we examine how NIR variability can help clarify the discrepancies between optical and X-ray classifications. Using the 14-year multiepoch UltraVISTA DR6 dataset in the YJHK_s bands, we constructed calibrated NIR light curves and quantified their variability through a set of metrics. Active galactic nucleus-like stochastic variability was identified by modeling the light curves with a damped random walk (DRW) process. We find that ∼7-17% of the 533 type 2 AGNs are variable in the NIR, with variability fractions increasing toward K_s, where the dusty torus dominates the emission. Based on the wavelength dependence of the DRW variability amplitude, we classify variable type 2 AGNs into disk-dominated, torus-dominated, and highly obscured groups. About one third of the X-ray unobscured (XR I) type 2 AGNs are variable in the NIR, consistent with misclassified weak type 1 or ``true type 2'' AGNs. On the other hand, 21.4% (30/140) of the X-ray obscured (XR II) type 2 AGNs show detectable variability in the NIR, most of them only in H or K_s, consistent with obscuration of the bluer (accretion disk) bands. Type 2 AGNs without X-ray counterparts (165) show the smallest fraction (3.6%) of variable objects. NIR variability provides an effective and independent diagnostic for confirming optical classifications and for identifying weak or misclassified type 1 AGNs in deep extragalactic surveys.

Abstract We experimentally determined the multiaxial strength of weak layers of buried surface hoar using displacement‐controlled tests under combined normal and shear loading on a custom testing machine. We tested 63 samples from three different weak layers, with strengths ranging from 1 to 10 kPa with considerable scattering. While shear strength was lower than compressive strength (typically about one to two thirds), we did not observe the very low shear strengths implied by a Mohr‐Coulomb‐cap type of failure envelope. Instead, our data were better described by elliptical failure envelopes, consistent with numerical predictions for other weak layer types. Density and microstructural parameters were quantified from micro‐computed tomography. Bulk density alone did not predict strength or envelope shape, but the data are not yet sufficient to derive robust quantitative structure–property relations. The envelope shape also appeared to be unrelated to the elastic properties, indicating that different microstructural aspects might govern elasticity and strength.

Weak type (1,1) jump inequalities in a nonsymmetric Gaussian setting

Prioritizing the development of regional innovation ecosystems (RIE) is essential for advancing China’s innovation-driven strategy. This study investigates how combinations of innovation elements, namely resources, services, achievements, and environment, affect regional innovation performance. Drawing on both innovation value-chain and ecosystem perspectives, we analyze the data from 31 Chinese provinces using fuzzy-set qualitative comparative analysis (fsQCA) and artificial neural networks (ANN). Our findings identify five distinct configurations that lead to high innovation performance and three that result in low or medium performance. High performance configurations include: resource achievement dual drive, outcome driven, and resource driven. Low performance configurations include talent shortage type, service deficiency type, and resource service dual weakness type. These results illustrate the principle of equifinality, indicating that different regions can achieve similar innovation outcomes through different pathways, and they underscore both the substitutability of certain elements and the synergy among them. Theoretically, the study advances configurational approaches in innovation research by integrating ecological and value-chain perspectives. Practically, it provides differentiated policy insights, suggesting that regions should tailor their innovation strategies to leverage specific strengths and thereby foster high-performance outcomes. First published online 4 March 2026

The weak type (1, 1) bounds for the $$\rho$$-variation operator associated with the Poisson semigroup

Abstract Let be a Fourier integral operator of order associated with a canonical relation locally parametrised by a real‐phase function. A fundamental result due to Seeger, Sogge and Stein proved in the 90's gives the boundedness of from the Hardy space into . Additionally, it was shown by T. Tao the weak (1,1) type of . In this work, we establish the weak (1,1) boundedness of a Fourier integral operator of order when it has associated a canonical relation parametrised by a complex phase function. This result in the complex‐valued setting cannot be derived from its counterpart in the real‐valued case.

Let f∈L1(N), where N=L∞(Gm)⊗ˉM, Gm is a bounded Vilenkin group and M is a semifinite von Neumann algebra. We prove the noncommutative weak type maximal inequality ∥(Dn(f))n≥1∥Λ1,∞(N,ℓ∞)≤C∥f∥L1(N), where Dn(f) represents the Vilenkin derivative of the integral function If. The main strategy in the proof is to exploit the recent advances on the noncommutative Calderón–Zygmund decomposition established by Cadilhac, Conde-Alonso and Parcet.

In this paper, we provide boundedness of strong and weak types for the maximum operator $\mathcal{M}$ in the generalized weighted Morrey space $M_{p,\varphi}(\Gamma,w)$ defined on Carleson curves $\Gamma$ and the local generalized weighted Morrey space $LM_{p,\varphi}^{\{t_0\}}(\Gamma,w)$.

This study aims to typologize the Employment Policy for the Persons with Disabilities according to levels of user support and employer support.Public social expenditure data on these two dimensions from 32 OECD countries were analyzed using fuzzy-set ideal type analysis.Four types emerged: the User-Employer Support Integrated Type (US*ES), with high levels of both supports; the User-Centered Type (US*es), with relatively high user support; the Employer-Centered Type (us*ES), with relatively high employer support; and the Weak User-Employer Support Type (us*es), with low levels of both.

Single-parameter and dual-parameter salaries for employees in eight categories have been developed (using cognitive factors of education and ownership).These salaries are calculated for different annual salary fund sizes, different wage scales, and different economic sectors (mining companies, high-tech enterprises, knowledgeintensive industries, universities, and design organizations), as well as for different levels of demand for employees' intellectual labor.They correspond to a table of the magnitudes of the manifestations of levels of education, acquired skills, and levels of ownership.The new y-processes (VSA processes) considered are quantitatively justified based on costs; their meanings are constructed from the process context and from the meaning phrases of the expenditure zelements.Wage schedules (WS) are created based on the history of salary increases and periods of participation in investment projects.WSs can be created in such a way that they correspond to three levels of complexity of the work performed.The new y-processes (FSA processes) discussed are quantitatively justified by costs, their meanings are constructed from the context of the processes and from the meaning phrases of the cost z-elements.According to the Chaddock scale, the model weights w1=c 2 11=0.3081 2 ; w2=c 2 12=0.3081 2 ; w3=c 2 13=0.3204 2 ; w4=c 2 14=0.32040.1665; 0.18326961, 0.22127616, 0.19395216, you (used in the 1-parameter grid) belong to the weak connection type, which reflects the low quality of education in the Republic of Kazakhstan (how did the AI know this?). When you see the small values of the "educational weights" realize the insignificance of an individual's initial contribution to the piggy bank of lifelong acquisitions.There is a premonition of great effort to achieve w3=c 2 18=1.Two-, three-, and four-parameter TS are needed to increase the values of the applied weights so that they "shift" toward the right end of the interval (0.3; 0.5).In the articles, the AI did not perceive the paltry scales of the manifestation forces; only through the situation with the evaluation of the labor of subjects of human capital does the AI notice the need to "shift" toward the right end of the interval (0.3; 0.5).This is the specific language of artificial intelligence for describing the processes of remuneration of educated people and individuals who have achieved one or another level of real estate ownership.

Let L = − ∑ i , j = 1 n a i j D i D j L=-\sum _{i,j=1}^n a_{ij}D_iD_j be the elliptic operator in non-divergence form with smooth real coefficients satisfying uniformly elliptic condition. Let W W be the global non-negative adjoint solution. If W ∈ A 2 W\in A_2 , we prove that the Riesz transforms ∇ L − 1 2 \nabla L^{-\frac {1}{2}} is of weak type ( 1 , 1 ) (1,1) with respect to the measure W ( x ) d x W(x)dx . This, together with L W 2 L^2_W boundedness of Riesz transforms (see Luis Escauriaza, Pablo Hidalgo-Palencia, and Steve Hofmann [Vietnam J. Math. 52 (2024), pp. 1067–1096]), implies that the Riesz transforms are bounded in L W p L^p_W for 1 > p > 2 1>p>2 .

Abstract We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on $$L^p$$ for every $$p>1$$ , and of weak type (1, 1). We also prove necessary and sufficient conditions for the $$L^p$$ -boundedness of the extension of a class of Toeplitz-type operators.

In this paper we give a strong and weak type Guliyev-Spanne type boundedness criterion for the potential operator I in the local generalized weighted Morrey space LM {t0} p, (, w) and the generalized weighted Morrey space M p, (, w) defined on Carleson curves .For the operator I we establish necessary and sufficient conditions for the strong and LM {t0} p, (, w) and the strong and weak Guliyev-Spanne type boundedness and M p, (, w).

Multiple-term refinements and reverses of real power form for Young-type inequalities via weak submajorization type theorems

Relative (α,β,γ)-weak type related growth analysis of meromorphic function with respect to entire function

In this paper, we investigate the strong and weak type boundedness of the maximal operator in Musielak-Orlicz-Morrey spaces. As an application of this boundedness, we give a sufficient condition for the strong and weak Adams type boundedness of the Riesz potential in these spaces.

Although anomaly identification is essential for identifying infrequent occurrences, these methods frequently fall short in differentiating anomaly from noise. While they are related, anomaly detection is different from noise removal. While anomaly detection is a component of data analysis, noises are undesired objects that impede the process. Although noise can be represented as a weak type of anomaly, this does not imply that all noise is abnormal. The elimination and identification of noise is crucial for anomaly detection, even though it is true that the distinction between the two is not exact. To tackle the challenge of anomaly detection, researchers have come up with various machine learning and data-mining algorithms. However, these methods come with their own set of issues, like forcing data points into specific clusters, class dominance, local convergence, and being overly sensitive to how clusters are chosen. Additionally, it's been observed that the same technique can produce different results when used on different datasets. Identifying abnormalities in cloud servers is vital for maintaining data confidentiality, especially with the rise of massive data storage and access in cloud computing. The security systems developed in the early stages of this study are more effective than previous access control methods. However, those earlier methods assumed that cloud servers could be trusted. In reality, the server in this system might be untrustworthy, as it often manipulates encrypted data and can be caught doing so.

Unmanned aerial vehicles (UAVs) are widely utilized for environmental monitoring, precision agriculture, infrastructure inspection, and various defense missions, including reconnaissance and surveillance. Their cybersecurity is essential because any compromise of communication, navigation, or control systems can cause mission failure and introduce significant safety and security risks. Therefore, this paper examines the existing literature on UAV cybersecurity and highlights that most previous surveys focus on listing different types of attacks or communication weaknesses, rather than evaluating the problem from a control systems perspective. Considering control systems is important because the safety and performance of a UAV depend on how cyberattacks affect its sensing, decision-making, and actuation loops; modeling these attacks and their impact on system behavior provides a clearer foundation for designing secure, resilient, and stable control strategies. Based on a comprehensive review of the literature, it presents a mathematical framework for characterizing common cyberattacks on UAV communication and sensing layers, including time-delay switch, false data injection, denial of service, and replay attacks. To demonstrate the impacts of these attacks on UAV control systems, a simulation of a two-UAV leader-follower multi-agent system is conducted in MATLAB. Defense algorithms from the existing literature are then organized into a hierarchical framework of prevention, detection, and mitigation, with detection and mitigation further categorized into model-based, learning-based, and hybrid approaches that combine both. The paper concludes by summarizing key findings and highlighting challenges with current defense strategies, including those insufficiently addressed in existing research.