The sea urchin Arbacia spatuligera is an echinoid distributed in the Southeastern Pacific Ocean from Peru to Chile. This species was previously reported from the subtidal zone with a bathymetric distribution up to 30 m depth. In this work, 128 individuals were found in four mesophotic reefs along the central coast off Chile using closed-circuit rebreathers in technical diving at higher depths than previously, ranging from 36 to 63 m in depth. A population exhibits unexpected morphological characters, requiring an emended diagnosis and description of a new morphotype for A. spatuligera. These morphological traits are further discussed as potential ecophenotypic adaptations.

The role of capital in measuring resilience is investigated. Focusing on the current short-run and potential long-run growth paths of the economic system, we propose new indexes to separately measure adaptability and resistance to shocks, which are the essence of a system’s resilience. Capital dynamics during the transition and along the balanced growth path are used here instead of employment to represent the evolution of the size and composition of the economy. Our indexes measure adaptability and resistance by comparing the two capital growth rates. They are built by mimicking the average and variance of the difference in growth rates. In this new setting, investment and depreciation flows play an important role in explaining what the partial index of adaptability reveals. The available data on the USA and Spanish capital allow us to empirically compute the indexes and draw conclusions about their ability to resist shocks and absorb their effects. We conclude that the US economy is more adaptable and has a greater capacity to absorb impacts than the Spanish economy, but it is less resistant to disturbances.

This paper is concerned with the study on an open problem of classifying conformally flat minimal Legendrian submanifolds in the $(2n+1)$-dimensional unit sphere $\mathbb {S}^{2n+1}$ admitting a Sasakian structure $(\varphi,\,\xi,\,\eta,\,g)$ for $n\ge 3$, motivated by the classification of minimal Legendrian submanifolds with constant sectional curvature. First of all, we completely classify such Legendrian submanifolds by assuming that the tensor $K:=-\varphi h$ is semi-parallel, which is introduced as a natural extension of $C$-parallel second fundamental form $h$. Secondly, such submanifolds have also been determined under the condition that the Ricci tensor is semi-parallel, generalizing the Einstein condition. Finally, as direct consequences, new characterizations of the Calabi torus are presented.

Despite a decade-long bull market between the financial crisis and the COVID-19 recession, state defined benefit pension plans had accrued more than $1.37 trillion in unfunded liabilities. However, little work has investigated the actuarial sources of these unfunded liabilities. This paper uses original data hand collected from publicly available financial reports between 2000 and 2020 for 145 state-administered pension plans to determine the sources of unfunded liabilities. The largest unfunded liability contributor is investment experiences (when actual investment returns do not match assumed returns). The second and third largest contributors are changes to actuarial assumptions and expected changes (or interest accruing on existing unfunded liabilities). Benefit experience and legislative changes, demographic experience, and explicit funding shortfalls account for relatively little of the growth in unfunded liabilities. Moreover, the specific sources of unfunded liabilities are heterogeneous over time and across plans.

Taxonomic intricacies and high interspecific similarity have hampered the identification of scyllarid phyllosoma larvae to the species level. The pygmy locust lobster, Scyllarus pygmaeus, is distributed across the Mediterranean Sea and in the eastern Atlantic; however, its phyllosoma larvae were previously recorded only from the western Mediterranean. We employed DNA barcoding using the mitochondrial COI gene to identify S. pygmaeus phyllosoma collected from the offshore waters of the southeastern Mediterranean Sea and described its morphology. We further discuss the lack of genetic structure in S. pygmaeus with potential implications for species connectivity and conservation.

Normally, the reported gain of the microstrip patch antenna is within 8 dBi. Using properly located three shorting pins on three bisectors, the present work reports a method to convert the non-radiating TM11 mode of equilateral triangular patch antennas (ETPAs) to a deformed TM11 radiating mode. The boresight gain of ETPA operating in TM11 mode is enhanced from −10.75 to 12.1 dBi at 5.43 GHz. The boresight measured gain is further enhanced to 14.2 dBi at 5.52 GHz by using a triangular surface-mounted short horn (SMSH) of about ${{\lambda }}/5$ height. The aperture efficiency of the ETPA with the shorting pins is 84.2%. The aperture efficiency is further improved to 94.2% using the SMSH. The measured boresight cross-polarization and side-lobe level are −40 and −29 dB, respectively. The nature of the electricfield and surface current distribution is analyzed, using both the characteristic mode analysis method and high-frequency structure simulator, to understand the role of shorting pin and coaxial feed in converting the non-radiating TM11 mode to the radiating mode. A systematic design process also is presented for a fast design of shorting pin-loaded ETPA on the suitable substrate at a specified frequency.

In this paper, we study the $(s, C(s))$-Harnack inequality in a domain $G\subset \mathbb {R}^n$ for $s\in (0,1)$ and $C(s)\geq 1$ and present a series of inequalities related to $(s, C(s))$-Harnack functions and the Harnack metric. We also investigate the behavior of the Harnack metric under K-quasiconformal and K-quasiregular mappings, where $K\geq 1$. Finally, we provide a type of harmonic Schwarz lemma and improve the Schwarz–Pick estimate for a real-valued harmonic function.

In this paper, a hybrid approach organized in four phases is proposed to solve the multi-objective trajectory planning problem for industrial robots. In the first phase, a transcription of the original problem into a standard multi-objective parametric optimization problem is achieved by adopting an adequate parametrization scheme for the continuous robot configuration variables. Then, in the second phase, a global search is performed using a population-based search metaheuristic in order to build a first approximation of the Pareto front (PF). In the third phase, a local search is applied in the neighborhood of each solution of the PF approximation using a deterministic algorithm in order to generate new solutions. Finally, in the fourth phase, results of the global and local searches are gathered and postprocessed using a multi-objective direct search method to enhance the quality of compromise solutions and to converge toward the true optimal PF. By combining different optimization techniques, we intend not only to improve the overall search mechanism of the optimization strategy but also the resulting hybrid algorithm should keep the robustness of the population-based algorithm while enjoying the theoretical properties of convergence of the deterministic component. Also, the proposed approach is modular and flexible, and it can be implemented in different ways according to the applied techniques in the different phases. In this paper, we illustrate the efficiency of the hybrid framework by considering different techniques available in various numerical optimization libraries which are combined judiciously and tested on various case studies.

In this paper, we prove that the bound

\begin{equation*}\max \{ |8A-7A|,|5f(A)-4f(A)| \} \gg |A|^{\frac{3}{2} + \frac{1}{54}}\end{equation*}

$A \subset \mathbb R$

\begin{equation*}\max \{ |16A|, |A^{(16)}| \} \gg |A|^{\frac{3}{2} + c},\end{equation*}

$c\gt 0$

$\mathbb R$

$3/2$

\begin{equation*}|AA| \leq K|A| \implies \,\forall d \in \mathbb R \setminus \{0 \}, \,\, |\{(a,b) \in A \times A : a-b=d \}| \ll K^C |A|^{\frac{2}{3}-c^{\prime}},\end{equation*}

$c,C \gt 0$

We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an extrinsic catenary is a critical point of the potential functional, where we calculate the potential with the extrinsic distance to a fixed reference plane in the ambient Lorentzian space. We then characterize extrinsic catenaries in terms of their curvature and as a solution to a prescribed curvature problem involving certain vector fields. In addition, we prove that the generating curve of any minimal surface of revolution in the hyperbolic space is an extrinsic catenary with respect to an appropriate reference plane. Finally, we prove that one of the families of extrinsic catenaries admits an intrinsic characterization if we replace the extrinsic distance with the intrinsic length of horocycles orthogonal to a reference geodesic.