Refined Factorizations of Solvable Potentials

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse and Coulomb potentials to obtain a wide set of raising and lowering operators, and to show clearly the connection that link these systems.Comment: 11 pages, LaTeX file, no figure

Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant $\hbar ^{\prime}=\hbar /k$) at some {\em fixed} BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of ``crystalline'' eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter

SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems

We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential $A\rho^{2\zeta-2}-B\rho^{\zeta-2}$. We show that in these cases the non-compact (compact) algebra corresponds to so(2,1) (su(2))

p53 mutations in human cutaneous melanoma correlate with sun exposure but are not always involved in melanomagenesis

In melanoma, the relationship between sun exposure and the origin of mutations in either the N-ras oncogene or the p53 tumour-suppressor gene is not as clear as in other types of skin cancer. We have previously shown that mutations in the N-ras gene occur more frequently in melanomas originating from sun-exposed body sites, indicating that these mutations are UV induced. To investigate whether sun exposure also affects p53 in melanoma, we analysed 81 melanoma specimens for mutations in the p53 gene. The mutation frequency is higher than thus far reported: 17 specimens (21%) harbour one or more p53 mutations. Strikingly, 17 out of 22 mutations in p53 are of the C:G to T:A or CC:GG to TT:AA transitional type, strongly suggesting an aetiology involving UV exposure. Interestingly, the p53 mutation frequency in metastases was much lower than in primary tumours. In the case of metastases, a role for sun exposure was indicated by the finding that the mutations are present exclusively in skin metastases and not in internal metastases. Together with a relatively frequent occurrence of silent third-base pair mutations in primary melanomas, this indicates that the p53 mutations, at least in these tumours, have not contributed to melanomagenesis and may have originated after establishment of the primary tumour. 1999 Cancer Research Campaig

Modern education technologies: 21^stcentury trends and challenges

Since modern technologies produce new global education trends, education prospects redesign, and new opportunities and threats assessments are needed. The new educational technology development phase was researched as an answer to modern world challenges. The strategic priorities of education in the EU are analyzed. New technologies, practices, and related needs: financing, digital integration, accessibility, informational security were studied and generalized. Higher education key trends and their transformation in the context of the COVID-19 crisis new opportunities and threats were researched. The analysis of the seven years of NMC Horizon and other research emerging educational technologies adoption forecasts provided in the research shows significant discrepancies related to extreme uncertainty. Five educational trend groups from the NMC Horizon report 2020 were reviewed. The author defined the remote education tools and their importance on the example of the university providing online/mixed learning. The anonymous polls among lecturers and students performed in the spring of 2020 (just after the COVID-19 quarantine announcement) show the most highly demanded tools are Google Meet, email, specific learning systems such as Moodle. The barriers to fully-fledged remote education are technical problems and occasionally poor Internet connectivity. The participants are quite ready to learn and to use digital tools for education. However, the absence of live communication increases workload during online learning, and other factors arise as the factors lowering student activity. During severe transformation, the main tasks of education are accessibility and diversity.</jats:p

Modern education technologies: 21

Since modern technologies produce new global education trends, education prospects redesign, and new opportunities and threats assessments are needed. The new educational technology development phase was researched as an answer to modern world challenges. The strategic priorities of education in the EU are analyzed. New technologies, practices, and related needs: financing, digital integration, accessibility, informational security were studied and generalized. Higher education key trends and their transformation in the context of the COVID-19 crisis new opportunities and threats were researched. The analysis of the seven years of NMC Horizon and other research emerging educational technologies adoption forecasts provided in the research shows significant discrepancies related to extreme uncertainty. Five educational trend groups from the NMC Horizon report 2020 were reviewed. The author defined the remote education tools and their importance on the example of the university providing online/mixed learning. The anonymous polls among lecturers and students performed in the spring of 2020 (just after the COVID-19 quarantine announcement) show the most highly demanded tools are Google Meet, email, specific learning systems such as Moodle. The barriers to fully-fledged remote education are technical problems and occasionally poor Internet connectivity. The participants are quite ready to learn and to use digital tools for education. However, the absence of live communication increases workload during online learning, and other factors arise as the factors lowering student activity. During severe transformation, the main tasks of education are accessibility and diversity