On simultaneous representations of primes by binary quadratic forms

AbstractLet p ≡ ± 1 (mod 8) be a prime which is a quadratic residue modulo 7. Then p = M2 + 7N2, and knowing M and N makes it possible to “predict” whether p = A2 + 14B2 is solvable or p = 7C2 + 2D2 is solvable. More generally, let q and r be distinct primes, and let an integral solution of H2p = M2 + qN2 be known. Under appropriate assumptions, this information can be used to restrict the possible values of K for which K2q = A2 + qrB2 is solvable and the possible values of K′ for which K′2p = qC2 + rD2 is solvable. These restrictions exclude some of the binary quadratic forms in the principal genus of discriminant −4qr from representing p

A systematic review of quality of student experience in higher education

Purpose: The purpose of this paper is to identify and synthesize major streams of research on quality of student experience in higher education, in order to present an agenda for future research. Design/methodology/approach: A systematic review of high quality journals published during the period 2000 to 2014 in the areas of quality of student experience and higher education was performed. Findings: Findings highlight current research trends on the quality of student experience in higher education. Results show five prevailing research streams: 1) exploration of learning experience; 2) exploration of student experience; 3) gender differences in assessment of higher education experience; 4) improvement in quality of student experience, 5) student satisfaction with higher education experience. Research limitations/implications: The identification of the five research streams presented in the findings of this paper provide the basis for a synthesis of key issues identified within each research stream. These discussions, along with the identification of the purposes and limitations of existential research allow existential issues concerning research on quality of student experience in higher education to be addressed. Practical implications: Literature currently portrays the quality of student experience as a student-centric idea. Together with the purposes and limitations identified in existing research, the paper proposes an agenda for future research that increases the variety of research streams that is essential to provide a deeper understanding of the student experience to enhance the delivery of quality in higher education. Originality/value: The findings contribute to the research scene by providing important insights in terms of the current trends and focus of existing research in the area of quality of student experience in higher education

Moving boundary approximation for curved streamer ionization fronts: Solvability analysis

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.Comment: 22 pages, 6 figure

Understanding the relationships between tourists\u27 emotional experiences, perceived overall image, satisfaction, and intention to recommend

The purpose of this study is to empirically test an integrative model linking tourists’ emotional experiences, perceived overall image, satisfaction, and intention to recommend. The model was tested using data collected from domestic tourists visiting Sardinia, Italy. Results show that tourists’ emotional experiences act as antecedents of perceived overall image and satisfaction evaluations. In addition, overall image has a positive influence on tourist satisfaction and intention to recommend. The study expands current theorizations by examining the merits of emotions in tourist behavior models. From a practical perspective, the study offers important implications for destination marketers

Positive Integers Represented by Regular Primitive Positive-Definite Integral Ternary Quadratic Forms

In 1997 Jagy, Kaplansky and Schiemann determined that there are at most 913 (classes of) primitive, positive-definite, integral ternary quadratic forms ax2 + by2 + cz2 + dyz + ezx + fxy which are regular. In this paper the positive integers represented by these 913 ternary forms are given

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Logarithmic diffusion and porous media equations: a unified description

In this work we present the logarithmic diffusion equation as a limit case when the index that characterizes a nonlinear Fokker-Planck equation, in its diffusive term, goes to zero. A linear drift and a source term are considered in this equation. Its solution has a lorentzian form, consequently this equation characterizes a super diffusion like a L\'evy kind. In addition is obtained an equation that unifies the porous media and the logarithmic diffusion equations, including a generalized diffusion equation in fractal dimension. This unification is performed in the nonextensive thermostatistics context and increases the possibilities about the description of anomalous diffusive processes.Comment: 5 pages. To appear in Phys. Rev.

Understanding the Relationships between Tourists’ Emotional Experiences, Perceived Overall Image, Satisfaction, and Intention to Recommend

The purpose of this study is to empirically test an integrative model linking tourists' emotional experiences, perceived overall image, satisfaction, and intention to recommend. The model was tested using data collected from domestic tourists visiting Sardinia, Italy. Results show that tourists' emotional experiences act as antecedents of perceived overall image and satisfaction evaluations. In addition, overall image has a positive influence on tourist satisfaction and intention to recommend. The study expands current theorizations by examining the merits of emotions in tourist behavior models. From a practical perspective, the study offers important implications for destination marketers

Radio-frequency dressed state potentials for neutral atoms

Potentials for atoms can be created by external fields acting on properties like magnetic moment, charge, polarizability, or by oscillating fields which couple internal states. The most prominent realization of the latter is the optical dipole potential formed by coupling ground and electronically excited states of an atom with light. Here we present an experimental investigation of the remarkable properties of potentials derived from radio-frequency (RF) coupling between electronic ground states. The coupling is magnetic and the vector character allows to design state dependent potential landscapes. On atom chips this enables robust coherent atom manipulation on much smaller spatial scales than possible with static fields alone. We find no additional heating or collisional loss up to densities approaching $10^{15}$ atoms / cm$^3$ compared to static magnetic traps. We demonstrate the creation of Bose-Einstein condensates in RF potentials and investigate the difference in the interference between two independently created and two coherently split condensates in identical traps. All together this makes RF dressing a powerful new tool for micro manipulation of atomic and molecular systems