How large can the first eigenvalue be on a surface of genus two?

Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of a fixed area are known only in genera zero and one. We investigate the genus two case and conjecture that the first eigenvalue is maximized on a singular surface which is realized as a double branched covering over a sphere. The six ramification points are chosen in such a way that this surface has a complex structure of the Bolza surface. We prove that our conjecture follows from a lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann boundary value problem on a half-disk. The latter can be studied numerically, and we present conclusive evidence supporting the conjecture.Comment: 20 pages; 4 figure

The Future of Clinical Leadership: The Critical Role of Front-Line Doctors

While people usually associate leadership with people with formal authority over organizations, front-line doctors play critical leadership roles today. We survey empirical studies in top management journals that speak to the role of front-line doctors in the implementation of service improvement initiatives. Front-line doctors can both drive and block change from within their organizations. In addition, doctors play critical roles in leading across professional groups, coordinating the input and work of different professionals. The leadership roles of front line doctors can impact whether and how health systems improve and learn, and how they perform. Harnessing the productive leadership potential of front-line doctors today is critical to creating a high performing, sustainable health care system. What are the new findings? •Generates knowledge of how front-line doctors play leadership roles in health care organizations •Highlights two leadership roles that front-line doctors play: driving and blocking organizational changes, and playing roles as leaders across professional groups in the context of service improvement initiatives •Offers suggestions backed by qualitative research of how people in formal leadership roles and front-line doctors themselves can harness the leadership potential of front-line doctors to improve health care organizations How might it impact on clinical practice in the near future? •By offering suggestions of how the leadership potential of front-line doctors can be harnessed, it has the potential to enable or inspire doctors to make changes in their organizations that can positively impact clinical practic

Effect of Pt doping on the critical temperature and upper critical field in YNi2-xPtxB2C (x=0-0.2)

We investigate the evolution of superconducting properties by doping non-magnetic impurity in single crystals of YNi2-xPtxB2C (x=0-0.2). With increasing Pt doping the critical temperature (Tc) monotonically decreases from 15.85K and saturates to a value ~13K for x>0.14. However, unlike conventional s-wave superconductors, the upper critical field (HC2) along both crystallographic directions a and c decreases with increasing Pt doping. Specific heat measurements show that the density of states (N(EF)) at the Fermi level (EF) and the Debye temperatures (Theta_D) in this series remains constant within the error bars of our measurement. We explain our results based on the increase in intraband scattering in the multiband superconductor YNi2B2C.Comment: ps file with figure

Conforming Finite Element Function Spaces in Four Dimensions, Part II: The Pentatope and Tetrahedral Prism

In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite element function spaces that maintain conformity with infinite-dimensional spaces of a carefully chosen de Rham complex. This paper is a natural extension of the companion paper entitled "Conforming Finite Element Function Spaces in Four Dimensions, Part I: Foundational Principles and the Tesseract" by Nigam and Williams, (2023). In contrast to Part I, in this paper we focus on two of the most popular elements which do not possess a full tensor-product structure in all four coordinate directions. We note that these elements appear frequently in existing space-time finite element methods. In order to build our finite element spaces, we utilize powerful techniques from the recently developed 'Finite Element Exterior Calculus'. Subsequently, we translate our results into the well-known language of linear algebra (vectors and matrices) in order to facilitate implementation by scientists and engineers.Comment: 44 pages, 2 figures, 1 tabl

Conforming Finite Element Function Spaces in Four Dimensions, Part 1: Foundational Principles and the Tesseract

The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element methods which often must satisfy an inf-sup condition in order to ensure stability. With this in mind, the primary objective of this paper and a companion paper is to provide a wide range of explicitly stated, conforming, finite element spaces in four-dimensions. In this paper, we construct explicit high-order conforming finite elements on 4-cubes (tesseracts); our construction uses tools from the recently developed `Finite Element Exterior Calculus'. With a focus on practical implementation, we provide details including Piola-type transformations, and explicit expressions for the volumetric, facet, face, edge, and vertex degrees of freedom. In addition, we establish important theoretical properties, such as the exactness of the finite element sequences, and the unisolvence of the degrees of freedom.Comment: 35 pages, 1 figure, 1 tabl

Core Vocabulary Intervention for Language-delayed Kindergarten Students Using Augmentative and Alternative Communication

The purpose of this study was to measure the impact of core vocabulary selection and the subsequent usage of a prescribed core vocabulary intervention over a period of one trimester (13-week period) and to report its impact on the overall communicative effectiveness of kindergarten students with language delay using augmentative and alternative communication (AAC). Study participants were provided with a pretest, speech and language therapy sessions in which intervention took place, and a posttest, which was administered by a speech–language pathologist. Intervention implementation commenced at the beginning of the school year and extended through the end of the trimester.13-week period. Data were examined at weekly intervals throughout the trimester. Analysis of the data determined the effect of selecting and using a core vocabulary intervention on overall communication in AAC users exhibiting language delay. The treatment group (n=15) received core vocabulary intervention in a naturalistic, aided-language environment, with modeling for the use of core vocabulary words. Acquisition of and significant improvement in core vocabulary usage was noticed, along with an increase in expressive language skills in line with individualized education plan (IEP) goals. The implications of core vocabulary intervention in the enhancement of language skills for Kindergarten-aged children who use AAC are discussed. Keywords: core vocabulary intervention, language-delayed, kindergarten, augmentative and alternative communication, language interventio