Remarks on the boundary set of spectral equipartitions

Given a bounded open set $\Omega$ in $\mathbb{R}^n$ (or a compact Riemannian manifold with boundary), and a partition of $\Omega$ by $k$ open sets $\omega_j$, we consider the quantity $\max_j \lambda(\omega_j)$, where $\lambda(\omega_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $\omega_j$. We denote by $\mathfrak{L}_k(\Omega)$ the infimum of $\max_j \lambda(\omega_j)$ over all $k$-partitions. A minimal $k$-partition is a partition which realizes the infimum. The purpose of this paper is to revisit properties of nodal sets and to explore if they are also true for minimal partitions, or more generally for spectral equipartitions. We focus on the length of the boundary set of the partition in the 2-dimensional situation.Comment: Final version to appear in the Philosophical Transactions of the Royal Society

Algorithmic Information Theory and Foundations of Probability

The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed

The Language of Man and the Language of God in George Herbert\u27s Religious Poetry

According to Burckhardt, the Reformation was an escape from discipline. The Reformation changed both the cultural and the religious reality of early modern Europe. Reformation theology and the new Renaissance understanding of self and of individuality required a radically new language in which to address God and at the same time demand a response. Medieval rhetoric of praise could no longer sustain the versatility of the Renaissance reader and could not provide the medium of searching for that response. The poetry of the metaphysical poets, Herbert in particular, bridges Christian discourse, rhetorical strategies, moral expression, radical dissention. Herbert was an orator and a theologian. Just as he distinguished between a secular, political world and a world of praise and divinity, he recognized overtones of divine language and human language. For Herbert, human discourse explicates processes of communication, questioning, irresolution, and doubt. It is essentially a conditional language that creates spaces within which the speaker can complain and criticize as if complaining and criticism were possible. The strategy of if\u27 in Herbert\u27s The Temple is to rewrite the stories that reader and speaker already know in a way that makes them accessible to experience. Thus Herbert encourages the reader to grasp the humanity of the speaker\u27s voice beyond theological dogma. The yearning and desire in Herbert\u27s if\u27 language confront the stable fixity of divine must language. In one of his early essays dealing with language, Walter Benjamin discuss fallen human language and language as such. His distinctions pertain to the function of language as freeing agent. In language, God has relieved man of divine actuality and let him be creative. Along the same lines, Herbert tries to explicate the adequacy of fallen language to serve as a medium of speaking and writing. His plea is that if we could only hear, and if we could only spell, we would have access to the stable and fixed language of God; but such access is in fact impossible to human beings. However, when humans speak and write, they transform the Word into a meaningful experience, and Herbert\u27s poetry is an exercise in articulating that process

A Formula of Newton

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73126/1/j.1949-8594.1974.tb09188.x.pd

Professional Realization and Label Market Problems – Nursing Program Student Survey

Given the shortage of nurses in Bulgaria, there stands at the forefront need of attracting of well-trained health care professionals to take care of the patients.It is beneficial for employers to be informed about student attitudes when choosing a job. Objective: The aim of the study was to explore the preconceptions of students in "Nurse" in the fourth course on professional realization and to give recommendations to the users of the staff.Methods: An anonymous survey was conducted amongst fourth year student nurses. Respondents were (52 students, aged 20 – 36).Results: The opinion of the students about sector, the therapeutic unit, the age group of patients with whom they would like to work, the preferences for work shifts, and their motivation to improve their qualification were investigated.The analysis of the results showed strong motivation and willingness to practice the profession - (94.23%) and improvement of competences through courses, specializations, etc. - (80.76%) and continuing education in a Master's degree (57.69%). The majority of the respondents (82.69%) pointed out as motivation for work the remuneration for the work done adequately.The analysis of the results revealed some worrying trends - the most preferred countries for practicing the profession are: Germany - (59.61%), USA - (17.30%), UK - (15.38).It was found that 15.38% of the respondents stated willingness for Continuing education abroad.Conclusion: In view of the increasing migration in countries in and outside the European Union, there are still reserves to improve the recruitment of staff in Bulgaria. It is extremely important to "rejuvenate" the aging population of nurses.The specificity of work and delicacy in serving sick people is a challenge for newly-educated nurses looking for better pay for their work and satisfaction with practicing the profession

Tracing organic matter composition and distribution and its role on arsenic release in shallow Cambodian groundwaters

Biogeochemical processes that utilize dissolved organic carbon are widely thought to be responsible for the liberation of arsenic from sediments to shallow groundwater in south and southeast Asia. The accumulation of this known carcinogen to hazardously high concentrations has occurred in the primary source of drinking water in large parts of densely populated countries in this region. Both surface and sedimentary sources of organic matter have been suggested to contribute dissolved organic carbon in these aquifers. However, identification of the source of organic carbon responsible for driving arsenic release remains enigmatic and even controversial. Here, we provide the most extensive interrogation to date of the isotopic signature of ground and surface waters at a known arsenic hotspot in Cambodia. We present tritium and radiocarbon data that demonstrates that recharge through ponds and/or clay windows can transport young, surface derived organic matter in to groundwater to depths of 44 m under natural flow conditions. Young organic matter dominates the dissolved organic carbon pool in groundwater that is in close proximity to these surface water sources and we suggest this is likely a regional relationship. In locations distal to surface water contact, dissolved organic carbon represents a mixture of both young surface and older sedimentary derived organic matter. Ground-surface water interaction therefore strongly influences the average dissolved organic carbon age and how this is distributed spatially across the field site. Arsenic mobilization rates appear to be controlled by the age of dissolved organic matter present in these groundwaters. Arsenic concentrations in shallow groundwaters (< 20 m) increase by 1 μg/l for every year increase in dissolved organic carbon age compared to only 0.25 μg/l for every year increase in dissolved organic carbon age in deeper (> 20 m) groundwaters. We suggest that, while the rate of arsenic release is greatest in shallow aquifer sediments, arsenic release also occurs in deeper aquifer sediments and as such remains an important process in controlling the spatial distribution of arsenic in the groundwaters of SE Asia. Our findings suggest that any anthropogenic activities that alter the source of groundwater recharge or the timescales over which recharge takes place may also drive changes in the natural composition of dissolved organic carbon in these groundwaters. Such changes have the potential to influence both the spatial and temporal evolution of the current groundwater arsenic hazard in this region

Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio

Contrasting Sorption Behaviours Affecting Groundwater Arsenic Concentration in Kandal Province, Cambodia

Natural arsenic (As) contamination of groundwater which provides drinking water and/or irrigation supplies remains a major public health issue, particularly in South and Southeast Asia. A number of studies have evaluated various aspects of the biogeochemical controls on As mobilization in aquifers typical to this region, however many are predicated on the assumption that key biogeochemical processes may be deduced by sampled water chemistry. The validity of this assumption has not been clearly established even though the role of sorption/desorption of As and other heavy metals onto Fe/Mn (hydr)oxides is an important control in As mobilization. Here, selective chemical extractions of sand-rich and clay-rich sediments from an As-affected aquifer in Kandal Province, Cambodia, were undertaken to explore the potential role of partial re-equilibrium through sorption/desorption reactions of As and related solutes (Fe, Mn and P) between groundwater and the associated solid aquifer matrix. In general, groundwater As is strongly affected by both pH and Eh throughout the study area. However, contrasting sorption behaviour is observed in two distinct sand-dominated (T-Sand) and clay dominated (T-Clay) transects, and plausibly attributed to differing dominant lithologies, biogeochemical and/or hydrogeological conditions. Sorption/desorption processes appear to be re-setting groundwater As concentrations in both transects, but to varying extents and in different ways. In T-Sand, which is typically highly reducing, correlations suggest that dissolved As may be sequestered by sorption/re-adsorption to Fe-bearing mineral phases and/or sedimentary organic matter; in T-Clay Eh is a major control on As mobilization although binding/occlusion of Fe-bearing minerals to sedimentary organic matter may also occur. Multiple linear regression analysis was conducted with groups categorised by transect and by Eh, and the output correlations support the contrasting sorption behaviours encountered in this study area. Irrespective of transect, however, the key biogeochemical processes which initially control As mobilization in such aquifers, may be “masked” by the re-setting of As concentrations through in-aquifer sorption/desorption processes

Un esquema para analizar los enunciados de los estudiantes en contextos de invención de problemas

The problem posing is considered as an important activity in the formation of mathematical skills of students, so they have made efforts to study it as a process of instruction in math classes; however, few investigations addressed strategies designed to assess student productions at this type of task. Thus, the construction and implementation of a analyses scheme that was used in a broader research study that aimed to characterize the arithmetic performance of a group of talented students in mathematics is presented. To do an analysis of the study variables of arithmetic problems and a study of the tools used in previous research was conducted, which allowed define three categories of analysis and in each study variables. The results show the feasibility of such a scheme to characterize the problems invented by students, identify different levels of complexity in the same and to assess the degree of profundity and appropriation of the knowledge learned.La invención de problemas es considerada como una actividad importante en la formación de habilidades matemáticas de los estudiantes, por lo que se han hecho esfuerzos por estudiarla como proceso de instrucción en clases de matemática; sin embargo, pocas investigaciones abordan estrategias que permitan valorar las producciones de estudiantes ante este tipo de tareas. Así, se presenta la construcción y puesta en práctica de un esquema de análisis que fue empleado en un estudio más amplio de investigación que pretendía caracterizar la actuación aritmética de un grupo de estudiantes con talento en matemática. Para ello, se realizó un análisis de las variables de estudio de los problemas aritméticos y un estudio de las herramientas empleadas en investigaciones previas, las cuales permitieron definir tres categorías de análisis y en cada una de ellas variables de estudio. Los resultados muestran la viabilidad de dicho esquema para caracterizar los problemas inventados por el estudiantado, para identificar diferentes niveles de complejidad en estos y para valorar el grado de profundización y apropiación de los conocimientos aprendidos