The Dynamical Mordell-Lang problem

Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a closed subset of X, and let x be a point on X. We show that the set S consisting of all nonnegative integers n such that f^n(x) is in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational self-map map f on X, any subvariety Y of X, and any point x in X whose orbit under f is in the domain of definition for f, the set S is a finite union of arithmetic progressions together with a set of Banach density zero. We prove a similar result for the backward orbit of a point

Intersections of orbits of self-maps with subgroups in semiabelian varieties

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$, endowed with a rational self-map $\Phi$. Let $\alpha\in G(K)$ and let $\Gamma\subseteq G(K)$ be a finitely generated subgroup. We show that the set $\{n\in\mathbb{N}\colon \Phi^n(\alpha)\in \Gamma\}$ is a union of finitely many arithmetic progressions along with a set of Banach density equal to $0$. In addition, assuming $\Phi$ is regular, we prove that the set $S$ must be finite.Comment: 12 page

Investigating students seriousness during selected conceptual inventory surveys

Conceptual inventory surveys are routinely used in education research to identify student learning needs and assess instructional practices. Students might not fully engage with these instruments because of the low stakes attached to them. This paper explores tests that can be used to estimate the percentage of students in a population who might not have taken such surveys seriously. These three seriousness tests are the pattern recognition test, the easy questions test, and the uncommon answers test. These three tests are applied to sets of students who were assessed either by the Force Concept Inventory, the Conceptual Survey of Electricity and Magnetism, or the Brief Electricity and Magnetism Assessment. The results of our investigation are compared to computer simulated populations of random answers.Comment: 8 pages; submitted to Phys Rev PE

Stochastic simplified modelling of abrasive waterjet footprints

Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet, and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within<8%. These advances could enable abrasive micro-waterjet technology as a suitable technology for controlled-depth milling

A brief review of the literature on the malignant ureteral obstruction

Malignant ureteral obstruction (MUO) caused by a primarily urological tumor or secondary to a late-stage malignancy can be difficult for the urologist to manage. Due to a lack of clinical data on the management of MUO, every case is particular and should be aborted individually. Lack of specific treatment, either palliative or definitive, can severely damage renal function and lifetime expectancy in patients, causing even more damage that could otherwise be avoided. Prompt management directed at the recovery of renal function is the main goal in such cases. Even after urinary flow is restored, life threatening post-obstructive diuresis needs to be managed

The importance of early arthritis in patients with rheumatoid arthritis

Rheumatoid arthritis (RA) is a systemic inflammatory disorder that manifests predominantly in the synovial joint, where it causes a chronic inflammatory process, leading to early osteoarticular destructions. These destructions are progressive and irreversible, generating a significant functional deficiency. During the last years, the diagnostic approach of RA has focused on early arthritis. Early arthritis can develop into established RA or another established arthropathy, like systemic lupus erythematosus or psoriatic arthritis. It can have a spontaneous resolution or may remain undifferentiated for indefinite periods of time. The management of early arthritis has changed considerably in the past few years, under the influence of new concepts of diagnosis and new effective therapies. The treatment goal of early arthritis should now be the clinical remission and prevention of joint destruction. Methotrexate is the first line of therapy, used to treat early arthralgia and to reverse or limit impending exacerbation to RA. Biological treatment is used as a second line therapy in patients with severe disease who do not respond or have a contraindication to disease-modifying antirheumatic drugs (DMARDs). Patients with early arthritis should usually be identified and directed to rheumatologists to confirm the presence of arthritis, and to establish the correct diagnosis plus to initiate the proper treatment strategies