A Survey on the Ternary Purely Exponential Diophantine Equation ax+by=cza^x + b^y = c^z

Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions $(x,y,z)$ of the ternary purely exponential diophantine equation $a^x + b^y = c^z$

Langmuir-Maxwell and Langmuir-Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics

The simulation of nonequilibrium thermal gas flow is important for the aerothermodynamic design of re-entry and other high-altitude vehicles. In computational fluid dynamics, the accuracy of the solution to the Navier–Stokes–Fourier (N–S–F) equations depends on the accuracy of the surface boundary conditions. We propose new boundary conditions (called the Langmuir–Maxwell and the Langmuir–Smoluchowski conditions), for use with the N–S–F equations, which combine the Langmuir surface adsorption isotherm with the Maxwell/Smoluchowski slip/jump conditions in order to capture some of the physical processes involved in gas flow over a surface. These new conditions are validated for flat plate flow, circular cylinder in cross-flow, and the flow over a sharp wedge for Mach numbers ranging from 6 to 24, and for argon and nitrogen as the working gases. Our simulation results show that the new boundary conditions give better predictions for the surface pressures, compared with published experimental and DSMC data

On a conjecture concerning the number of solutions to ax+by=cza^x+b^y=c^z, II

Let $a$, $b$, $c$ be fixed coprime positive integers with $\min\{ a,b,c \} >1$, $a<b$. Let $N(a,b,c)$ denote the number of positive integer solutions $(x,y,z)$ of the equation $a^x + b^y = c^z$. We show that if $(a,b,c)$ is a triple of distinct primes for which $N(a,b,c)>1$ and $(a,b,c)$ is not one of the six known such triples then we must have $a=2$, $b \equiv 1 \bmod 48$, $c \equiv 17 \mod 48$, $2 \mid v_2(p-1) \le v_2(q-1)$ where $v_2(n)$ satisfies $2^{v_2(n)} \parallel n$, at least one of the multiplicative orders $u_q(p)$ or $u_p(q)$ must be odd where $u_p(n)$ is the least integer $t$ such that $n^t \equiv 1 \bmod p$, and 2 must be an octic residue modulo $q$ except for two specific cases. These results support a conjecture put forward in [26] and improve results in [15]

Words are Malleable: Computing Semantic Shifts in Political and Media Discourse

Recently, researchers started to pay attention to the detection of temporal shifts in the meaning of words. However, most (if not all) of these approaches restricted their efforts to uncovering change over time, thus neglecting other valuable dimensions such as social or political variability. We propose an approach for detecting semantic shifts between different viewpoints--broadly defined as a set of texts that share a specific metadata feature, which can be a time-period, but also a social entity such as a political party. For each viewpoint, we learn a semantic space in which each word is represented as a low dimensional neural embedded vector. The challenge is to compare the meaning of a word in one space to its meaning in another space and measure the size of the semantic shifts. We compare the effectiveness of a measure based on optimal transformations between the two spaces with a measure based on the similarity of the neighbors of the word in the respective spaces. Our experiments demonstrate that the combination of these two performs best. We show that the semantic shifts not only occur over time, but also along different viewpoints in a short period of time. For evaluation, we demonstrate how this approach captures meaningful semantic shifts and can help improve other tasks such as the contrastive viewpoint summarization and ideology detection (measured as classification accuracy) in political texts. We also show that the two laws of semantic change which were empirically shown to hold for temporal shifts also hold for shifts across viewpoints. These laws state that frequent words are less likely to shift meaning while words with many senses are more likely to do so.Comment: In Proceedings of the 26th ACM International on Conference on Information and Knowledge Management (CIKM2017

Merger as Intermittent Accretion

The Self-Similar Secondary Infall Model (SSIM) is modified to simulate a merger event. The model encompass spherical versions of tidal stripping and dynamical friction that agrees with the Syer & White merger paradigm's behaviour. The SSIM shows robustness in absorbing even comparable mass perturbations and returning to its original state. It suggests the approach to be invertible and allows to consider accretion as smooth mass inflow merging and mergers as intermittent mass inflow accretion.Comment: letter accepted by A&A 29/09/08, 4 pages, colour figure

A method for improving the performance of gradient systems for diffusion-weighted MRI

The MR signal is sensitive to diffusion. This effect can be increased by the use of large, balanced bipolar gradients. The gradient systems of MR scanners are calibrated at installation and during regular servicing visits. Because the measured apparent diffusion constant (ADC) depends on the square of the amplitude of the diffusion sensitizing gradients, errors in the gradient calibration are exaggerated. If the error is varying among the different gradient axes, it will affect the estimated degree of anisotropy. To assess the gradient calibration accuracy in a whole-body MRI scanner, ADC values were calculated for a uniform water phantom along each gradient direction while monitoring the temperature. Knowledge of the temperature allows the expected diffusion constant of water to be calculated independent of the MRI measurement. It was found that the gradient axes (±x, ±y, ±z) were calibrated differently, resulting in offset ADC values. A method is presented to rescale the amplitude of each of the six principal gradient axes within the MR pulse sequence. The scaling factor is the square root of the ratio of the expected and observed diffusion constants. In addition, fiber tracking results in the human brain were noticeably affected by improving the gradient system calibration. Magn Reson Med 58:763–768, 2007. © 2007 Wiley-Liss, Inc

Microstructural parameter estimation in vivo using diffusion MRI and structured prior information.

Diffusion MRI has recently been used with detailed models to probe tissue microstructure. Much of this work has been performed ex vivo with powerful scanner hardware, to gain sensitivity to parameters such as axon radius. By contrast, performing microstructure imaging on clinical scanners is extremely challenging

On the universality of density profiles

We use the secondary infall model described in Del Popolo (2009), which takes into account the effect of dynamical friction, ordered and random angular momentum, baryons adiabatic contraction and dark matter baryons interplay, to study how in- ner slopes of relaxed LCDM dark matter (DM) halos with and without baryons (baryons+DM, and pure DM) depend on redshift and on halo mass. We apply the quoted method to structures on galactic scales and clusters of galaxies scales. We find that the inner logarithmic density slope, of dark matter halos with baryons has a significant dependence on halo mass and redshift with slopes ranging from 0 for dwarf galaxies to 0.4 for objects of M = 10^13M_solar and 0.94 for M = 10^15M_solar clusters of galaxies. Structures slopes increase with increasing redshift and this trend reduces going from galaxies to clusters. In the case of density profiles constituted just of dark matter the mass and redshift dependence of slope is very slight. In this last case, we used the Merrit et al. (2006) analysis who compared N-body density profiles with various parametric models finding systematic variation in profile shape with halo mass. This last analysis suggests that the galaxy-sized halos obtained with our model have a different shape parameter, i.e. a different mass distribution, than the cluster-sized halos, obtained with the same model. The results of the present paper argue against universality of density profiles constituted by dark matter and baryons and confirm claims of a systematic variation in profile shape with halo mass, for dark matter halos.Comment: 11 pages, 5 figure

Lingual Salt Glands in Crocodylus acutus and C. johnstoni and Their Absence from Alligator mississipiensis and Caiman crocodilus

1. Lingual salt glands, secreting hyperosmotic Na/K solutions in response to methacholine, are present in Crocodylus acutus and C. johnstoni but apparently absent from the alligatorids, Alligator mississipiensis and Caiman crocodilus. 2. Both secretory rates (6-20 [micro-mol/100 g-h) and concentrations (450-600 mM Na) of glandular secretions are essentially identical in the marine/estuarine C. acutus and C. porosus and significantly higher than in the freshwater C. johnstoni (1-2 micro-mol/100 g-h; 320-420 mM Na). 3. Lingual glands in Alligator secrete isosmotic Na/K at low rates (1-2 micro-mol/100 g-h) while those of Caiman show no response to methacholine. 4. The physiological contrast between alligatorids and crocodylids is reflected in distinct differences in the superficial appearance of the tongue and lingual pores. 5. It is postulated that the alligatorid condition of low secretory capacity and isosmotic secretion reflects the primitive salivary function of lingual glands from which the salt-secreting capability in crocodylids was derived

Cloud engineering is search based software engineering too

Many of the problems posed by the migration of computation to cloud platforms can be formulated and solved using techniques associated with Search Based Software Engineering (SBSE). Much of cloud software engineering involves problems of optimisation: performance, allocation, assignment and the dynamic balancing of resources to achieve pragmatic trade-offs between many competing technical and business objectives. SBSE is concerned with the application of computational search and optimisation to solve precisely these kinds of software engineering challenges. Interest in both cloud computing and SBSE has grown rapidly in the past five years, yet there has been little work on SBSE as a means of addressing cloud computing challenges. Like many computationally demanding activities, SBSE has the potential to benefit from the cloud; ‘SBSE in the cloud’. However, this paper focuses, instead, of the ways in which SBSE can benefit cloud computing. It thus develops the theme of ‘SBSE for the cloud’, formulating cloud computing challenges in ways that can be addressed using SBSE