In this paper, we study the behaviours of the commutators $[\vec b,\,T]$ generated by multilinear Calderón–Zygmund operators $T$ with $\vec b=(b_1,\,\ldots,\,b_m)\in L_{\rm loc}(\mathbb {R}^n)$ on weighted Hardy spaces. We show that for some $p_i\in (0,\,1]$ with $1/p=1/p_1+\cdots +1/p_m$, $\omega \in A_\infty$ and $b_i\in \mathcal {BMO}_{\omega,p_i}$ ($1\le i\le m$), which are a class of non-trivial subspaces of ${\rm BMO}$, the commutators $[\vec b,\,T]$ are bounded from $H^{p_1}(\omega )\times \cdots \times H^{p_m}(\omega )$ to $L^p(\omega )$. Meanwhile, we also establish the corresponding results for a class of maximal truncated multilinear commutators $T_{\vec b}^*$.

Let f be an isolated singularity at the origin of $\mathbb {C}^n$. One of many invariants that can be associated with f is its Łojasiewicz exponent $\mathcal {L}_0 (f)$, which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for $\mathcal {L}_0 (f)$ in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates.

We prove that the uncentered Hardy–Littlewood maximal operator is discontinuous on ${BMO}(\mathbb {R}^n)$ and maps ${VMO}(\mathbb {R}^n)$ to itself. A counterexample to the boundedness of the strong and directional maximal operators on ${BMO}(\mathbb {R}^n)$ is given, and properties of slices of ${BMO}(\mathbb {R}^n)$ functions are discussed.

We present a photogrammetric model and new line drawing of Sacul Stela 3 at the ancient Maya site of Sacul 1, Guatemala. Although virtually illegible in person and from photographs, the inscription on the eroded stela can largely be read or reconstructed in the 3D model. Our reading confirms a previous argument that the kingdom based at Sacul 1 was attacked in A.D. 779 by forces from the site of Ucanal. Traveling by night, warriors from Sacul retaliated with a raid at dawn next day on an unidentified site and, months later, followed up with an attack on Ucanal itself. The same narrative appears substantially on a well-known monument, Ixkun Stela 2, but there are differences between the two texts which suggest that Sacul and Ixkun had their own sculptors and record-keepers and which offer insights into the implications of verbs (pul, “to burn” and ch'ak, “to chop”) commonly attested in Classic Maya accounts of war. We then present the results of GIS analysis which suggests that the site area of El Rosario (between Sacul 1 and Ucanal) is an appealing candidate for the unidentified site mentioned in the stela text.

Professor Thomas James Fahy, consultant psychiatrist, who died on 9 January 2023, made substantial contributions to the development of psychiatry, medical teaching, psychiatric research, and post-graduate training in Ireland, England, and the United States. He was a Foundation Fellow of the Royal College of Psychiatrists and Founder Chairman of the Irish Psychiatric Training Committee. He served as Professor of Psychiatry at University College Galway from 1975 to 2001 and also served on the Medical Council and Medical Research Council, among other bodies. Professor Fahy’s research interests included depressive symptomatology, anxiety disorders, post-traumatic stress disorder, head injury, suicide, and electroconvulsive therapy. He was a compassionate doctor, an inspiring teacher, a witty speaker, and a superb ambassador for psychiatry in Ireland and beyond.

A novel parabolic dish solar concentrator based on the improved 3-RPS parallel manipulator to drive the reflective mirror facet is proposed and designed, which can not only automatically adjust the position and orientation of the reflective mirror facet but also have the advantages of independent drive, high stiffness and no cumulative error. Then, using the coordinate transformation matrixes of the novel parabolic dish solar tracking platform, the kinematics models of the 3-RPS parallel manipulators associated with the solar altitude and azimuth angles are established. The altitude and azimuth angles of the solar movement at the installation location are calculated according to the calculation formula of solar position. To solve the problem of too many telescopic rods of the 3-RPS parallel manipulator, a genetic algorithm is used to optimize the height of the concentrator’s center of mass. Then the ideal trajectory and attitude of each telescopic rod of the 3-RPS parallel manipulators at different times of the day can be obtained with the inverse kinematics. The particle swarm optimization (PSO)-proportional-integral-derivative (PID) controller, which uses PSO algorithm to tune PID parameters, is proposed for solar trajectory tracking of the novel parabolic dish solar concentrator. The visual simulation model of the parabolic dish system is established in Simscape Multibody, and the trajectory tracking control experiment is carried out. The experimental results show that the trajectory tracking error of the novel dish solar tracking platform can be within 2.6 mm by using the PSO-PID controller.

We consider the non-linear Schrödinger equation(Pμ)

\begin{equation*}\begin{array}{lc}-\Delta u + V(x) u = \mu f(u) + |u|^{2^*-2}u, &\end{array}\end{equation*}

$\mathbb{R}^N$

$N\geq3$

$f(s)/s$

Humanitarian visas provide one of few potential pathways to citizenship for foreign nationals victimized within the United States and are an important aspect of immigration law. Yet one form of humanitarian visas—T nonimmigrant status (T visa)—has received scant attention in the socio-legal studies literature. “T visas” were designed to aid survivors of human trafficking and, though the US government estimates that tens of thousands of individuals are trafficked in the United States every year, only 15 percent of the five thousand T visas available annually have been granted since the program’s inception in 2002. Why are T visas such an underutilized form of immigration relief? Drawing on twenty in-depth interviews with immigration lawyers, law enforcement personnel, and non-governmental organization service providers routinely involved in T visa applications, we find that the low rate of applications and approvals is driven by a combination of structural barriers and expansive discretion of key actors in the legal process to interpret and apply the law, which results in a narrow and often misinformed construction of victimhood. We add to the literature on the discretionary power of street-level bureaucrats to shape the law and determine how it is applied with considerable consequences for survivors of trafficking.

We analyze genitive of negation (GN) in Lithuanian. When the verb is negated, GN is realized on an object that would otherwise be realized as accusative. We demonstrate that Lithuanian GN is a syntactic (in line with Arkadiev 2016) and morphological phenomenon in contrast to Russian GN, whose realization is influenced by semantic factors (e.g. Kagan 2013). It differs from Russian (Pesetsky 1982) in that (i) it is always assigned to a DP which would otherwise bear structural accusative regardless of its semantic properties, and (ii) it cannot affect a structural nominative DP regardless of whether it is an external or internal argument. Lithuanian GN, in this respect, is similar to Polish GN (e.g. Przepiórkowski 2000, Witkoś 2008). We offer a three-layered approach to case, arguing that GN is a reflection of structural object case, assigned in syntax, then translated to morphological genitive case at PF and, finally, realized at Vocabulary Insertion (Halle & Marantz 1993). Thus, structural object case has two morphological realizations: as genitive under negation or as accusative in the absence of negation. Lithuanian also exhibits long-distance GN (Arkadiev 2016), showing that case boundaries can cross non-finite clauses without an overt CP element, suggesting these are not phases.