Guided Unfoldings for Finding Loops in Standard Term Rewriting

In this paper, we reconsider the unfolding-based technique that we have introduced previously for detecting loops in standard term rewriting. We improve it by guiding the unfolding process, using distinguished positions in the rewrite rules. This results in a depth-first computation of the unfoldings, whereas the original technique was breadth-first. We have implemented this new approach in our tool NTI and compared it to the previous one on a bunch of rewrite systems. The results we get are promising (better times, more successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. For models of a certain type, however, the equivalence may not hold as we discuss in this Letter. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.Comment: No figure

Relativistic confinement of neutral fermions with a trigonometric tangent potential

The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for $E=\pm mc^{2}$, the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential ($\sim \mathrm{tan} \gamma x$) is exactly solved and the complete set of solutions is discussed in some detail. It is revealed that this intrinsically relativistic and true confining potential is able to localize fermions into a region of space arbitrarily small without the menace of particle-antiparticle production.Comment: 12 page

Magnetoresistivity in a Tilted Magnetic Field in p-Si/SiGe/Si Heterostructures with an Anisotropic g-Factor: Part II

The magnetoresistance components $\rho_{xx}$ and $\rho_{xy}$ were measured in two p-Si/SiGe/Si quantum wells that have an anisotropic g-factor in a tilted magnetic field as a function of temperature, field and tilt angle. Activation energy measurements demonstrate the existence of a ferromagnetic-paramagnetic (F-P) transition for a sample with a hole density of $p$=2$\times10^{11}$\,cm$^{-2}$. This transition is due to crossing of the 0$\uparrow$ and 1$\downarrow$ Landau levels. However, in another sample, with $p$=7.2$\times10^{10}$\,cm$^{-2}$, the 0$\uparrow$ and 1$\downarrow$ Landau levels coincide for angles $\Theta$=0-70$^{\text{o}}$. Only for $\Theta$ > 70$^{\text{o}}$ do the levels start to diverge which, in turn, results in the energy gap opening.Comment: 5 pages, 6 figure

Provision of mental health care within primary care in Peru: A qualitative study exploring the perspectives of psychologists, primary health care providers, and patients.

Background: This study aimed to understand the offer of mental health care at the primary care level, collecting the views of psychologists, primary health care providers (PHCPs), and patients, with a focus on health services in which patients attend regularly and who present a higher prevalence of mental disorders. Methods: A qualitative study was conducted in antenatal care, tuberculosis, HIV/AIDS, and chronic diseases services from six primary health care centers. Semi-structured interviews were conducted with psychologists, PHCPs, and patients working in or attending the selected facilities.  Results: A total of 4 psychologists, 22 PHCPs, and 37 patients were interviewed. A high perceived need for mental health care was noted. PHCPs acknowledged the emotional impact physical health conditions have on their patients and mentioned that referral to psychologists was reserved only for serious problems. Their approach to emotional problems was providing emotional support (includes listening, talk about their patients' feelings, provide advice). PHCPs identified system-level barriers about the specialized mental health care, including a shortage of psychologists and an overwhelming demand, which results in brief consultations and lack in continuity of care. Psychologists focus their work on individual consultations; however, consultations were brief, did not follow a standardized model of care, and most patients attend only once. Psychologists also mentioned the lack of collaborative work among other healthcare providers. Despite these limitations, interviewed patients declared that they were willing to seek specialized care if advised and considered the psychologist's care provided as helpful; however, they recognized the stigmatization related to seeking mental health care. Conclusions: There is a perceived need of mental health care for primary care patients. To attend these needs, PHCPs provide emotional support and refer to psychology the most severe cases, while psychologists provide one-to-one consultations. Significant limitations in the care provided are discussed