The spectral function for Sturm-Liouville problems where the potential is of Wigner-von Neumann type or slowly decaying

We consider the linear, second-order, differential equation (∗) with the boundary condition (∗∗) We suppose that q(x) is real-valued, continuously differentiable and that q(x)→0 as x→∞ with q∉L1[0,∞). Our main object of study is the spectral function ρα(λ) associated with () and (). We derive a series expansion for this function, valid for λ⩾Λ0 where Λ0 is computable and establish a Λ1, also computable, such that () and () with α=0, have no points of spectral concentration for λ⩾Λ1. We illustrate our results with examples. In particular we consider the case of the Wigner–von Neumann potential

Functional specialization within rostral prefrontal cortex (Area 10): a meta-analysis

One of the least well understood regions of the human brain is rostral prefrontal cortex, approximating Brodmann's area 10. Here, we investigate the possibility that there are functional subdivisions within this region by conducting a meta-analysis of 104 functional neuroimaging studies (using positron emission tomography/functional magnetic resonance imaging). Studies involving working memory and episodic memory retrieval were disproportionately associated with lateral activations, whereas studies involving mentalizing (i.e., attending to one's own emotions and mental states or those of other agents) were disproportionately associated with medial activations. Functional variation was also observed along a rostral-caudal axis, with studies involving mentalizing yielding relatively caudal activations and studies involving multiple-task coordination yielding relatively rostral activations. A classification algorithm was trained to predict the task, given the coordinates of each activation peak. Performance was well above chance levels (74% for the three most common tasks; 45% across all eight tasks investigated) and generalized to data not included in the training set. These results point to considerable functional segregation within rostral prefrontal cortex

Higher derivatives of spectral functions associated with one-dimensional schrodinger operators

We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory

Peranan Poliembrioni Terhadap Produksi Benih Pada Tanaman Jeruk Siam (Citrus nobilis L.)

This study aims to determine the growth of polyembryonic seeds in Siamese oranges and to study the growth of seedlings from polyembryonic seeds which will be used as good seeds in overcoming the problem of availability of Siamese orange seeds. The research was carried out from May to October 2022 at the Green House of the Faculty of Agriculture, Sam Ratulangi University and Eris Village, Eris District. The research method used a randomized block design (RBD) with 5 treatments repeated 4 times and found a total of 20 treatments, namely Z11, Z12, Z13, Z14, P21, P22, P23, P24, P31, P32, P33, P34, B21, B22, B23 , B24, B31, B32, B33 and B34. Data analysis used ANOVA analysis (analysis of variance). If it has no effect, then proceed with the BNT test at the 5% test level. The results showed that the growth of Siamese orange sprouts resulted in the growth of embryos up to 6 intact in one seed. Polyembryony, the ability to germinate seeds above 80.00% is one of the conditions for seeds to be recommended for seed sources 20.95%

Interaction energy functional for lattice density functional theory: Applications to one-, two- and three-dimensional Hubbard models

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\gamma]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of $W$ is obtained throughout the domain of representability of $\gamma_{ij}$, including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for $W$. Goals and limitations of the different approximations are discussed.Comment: 25 pages and 8 figures, submitted to Phys. Rev.

On Entangled Multi-particle Systems in Bohmian Theory

Arguments are presented to show that in the case of entangled systems there are certain difficulties in implementing the usual Bohmian interpretation of the wave function in a straightforward manner. Specific examples are given.Comment: 7 page

Coronal Shock Waves, EUV waves, and their Relation to CMEs. II. Modeling MHD Shock Wave Propagation Along the Solar Surface, Using Nonlinear Geometrical Acoustics

We model the propagation of a coronal shock wave, using nonlinear geometrical acoustics. The method is based on the Wentzel-Kramers-Brillouin (WKB) approach and takes into account the main properties of nonlinear waves: i) dependence of the wave front velocity on the wave amplitude, ii) nonlinear dissipation of the wave energy, and iii) progressive increase in the duration of solitary shock waves. We address the method in detail and present results of the modeling of the propagation of shock-associated extreme-ultraviolet (EUV) waves as well as Moreton waves along the solar surface in the simplest solar corona model. The calculations reveal deceleration and lengthening of the waves. In contrast, waves considered in the linear approximation keep their length unchanged and slightly accelerate.Comment: 15 pages, 7 figures, accepted for publication in Solar Physic

Spin pumping and magnetization dynamics in metallic multilayers

We study the magnetization dynamics in thin ferromagnetic films and small ferromagnetic particles in contact with paramagnetic conductors. A moving magnetization vector causes \textquotedblleft pumping\textquotedblright of spins into adjacent nonmagnetic layers. This spin transfer affects the magnetization dynamics similar to the Landau-Lifshitz-Gilbert phenomenology. The additional Gilbert damping is significant for small ferromagnets, when the nonmagnetic layers efficiently relax the injected spins, but the effect is reduced when a spin accumulation build-up in the normal metal opposes the spin pumping. The damping enhancement is governed by (and, in turn, can be used to measure) the mixing conductance or spin-torque parameter of the ferromagnet--normal-metal interface. Our theoretical findings are confirmed by agreement with recent experiments in a variety of multilayer systems.Comment: 10 pages, 6 figure

Anomalous mid-twentieth century atmospheric circulation change over the South Atlantic compared to the last 6000 years

Determining the timing and impact of anthropogenic climate change in data-sparse regions is a considerable challenge. Arguably, nowhere is this more difficult than the Antarctic Peninsula and the subantarctic South Atlantic where observational records are relatively short but where high rates of warming have been experienced since records began. Here we interrogate recently developed monthly-resolved observational datasets from the Falkland Islands and South Georgia, and extend the records back using climate-sensitive peat growth over the past 6000 years. Investigating the subantarctic climate data with ERA-Interim and Twentieth Century Reanalysis, we find that a stepped increase in precipitation across the 1940s is related to a change in synoptic atmospheric circulation: a westward migration of quasi-permanent positive pressure anomalies in the South Atlantic has brought the subantarctic islands under the increased influence of meridional airflow associated with the Amundsen Sea Low. Analysis of three comprehensively multi-dated (using 14C and 137Cs) peat sequences across the two islands demonstrates unprecedented growth rates since the mid-twentieth century relative to the last 6000 years. Comparison to observational and reconstructed sea surface temperatures suggests this change is linked to a warming tropical Pacific Ocean. Our results imply 'modern' South Atlantic atmospheric circulation has not been under this configuration for millennia

Integrated market selection and production planning: Complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances