On the locus formed by the maximum heights of projectile motion with air resistance

We present an analysis on the geometrical place formed by the set of maxima of the trajectories of a projectile launched in a media with linear drag. Such a place, the locus of apexes, is written in term of the Lambert $W$ function in polar coordinates, confirming the special role played by this function in the problem. In order to characterize the locus, a study of its curvature is presented in two parameterizations, in terms of the launch angle and in the polar one. The angles of maximum curvature are compared with other important angles in the projectile problem. As an addendum, we find that the synchronous curve in this problem is a circle as in the drag-free case.Comment: 7 pages, 6 color eps figures. Synchronous curve added. Typos and style corrected

Dynamic paramagnon-polarons in altermagnets

The combined rotational and time-reversal symmetry breakings that define an altermagnet lead to an unusual d-wave (or g-wave) magnetization order parameter, which in turn can be modeled in terms of multipolar magnetic moments. Here, we show that such an altermagnetic order parameter couples to the dynamics of the lattice even in the absence of an external magnetic field. This coupling is analogous to the non-dissipative Hall viscosity and describes the stress generated by a time-varying strain under broken time-reversal symmetry. We demonstrate that this effect generates a hybridized paramagnon-polaron mode, which allows one to assess altermagnetic excitations directly from the phonon spectrum. Using a scaling analysis, we also demonstrate that the dynamic strain coupling strongly affects the altermagnetic phase boundary, but in different ways in the thermal and quantum regimes. In the ground state, we find that a hardening of the altermagnon mode leads to an extended altermagnetic ordered regime, whereas for non-zero temperatures, the softening of the phonon modes leads to increased fluctuations that lower the altermagnetic transition temperature. We also discuss the application of these results to standard ferromagnetic systems.Comment: 14 pages, 7 figure

Fuel Cell Power Model Version 2: Startup Guide, System Designs, and Case Studies. Modeling Electricity, Heat, and Hydrogen Generation from Fuel Cell-Based Distributed Energy Systems

This guide helps users get started with the U.S. Department of Energy/National Renewable Energy Laboratory Fuel Cell Power (FCPower) Model Version 2, which is a Microsoft Excel workbook that analyzes the technical and economic aspects of high-temperature fuel cell-based distributed energy systems with the aim of providing consistent, transparent, comparable results. This type of energy system would provide onsite-generated heat and electricity to large end users such as hospitals and office complexes. The hydrogen produced could be used for fueling vehicles or stored for later conversion to electricity

Prognostic factors in high and intermediate grade non-Hodgkin's lymphoma.

An analysis of prognostic factors has been performed on 260 patients with high and intermediate grade non-Hodgkin's lymphoma (NHL) treated over an 11-year period between 1975 and 1986. The overall 5-year survival rate was 50% with a median follow-up of 72 months. Over 20 clinical, radiological and laboratory parameters have been studied, including variables reported to be important indicators of prognosis in previous series, and these variables have been subjected to univariate and multivariate analysis. Attainment of complete remission (CR) was the most important predictor of overall survival, low serum lactate dehydrogenase (LDH), limited stage disease and a high serum albumin were also independently associated with prolonged survival in multivariate analysis. After removing remission status from the model, Ann Arbor clinical stage became the most significant pre-treatment prognostic indicator. Sixty-five per cent of patients achieved CR, and a discriminant analysis showed that failure to attain CR was associated with advanced stage disease, constitutional symptoms, increasing patient age, a low serum albumin and the presence of bulk disease. Advanced clinical stage and an elevated serum LDH predicted independently for a poor relapse-free survival, and reduced overall survival following CR. There was no significant correlation between histological subtype in the Kiel classification and prognosis. This study confirms the prognostic significance of remission status and Ann Arbor clinical stage, and illustrates additional factors including serum levels of albumin and LDH, which serve to enhance the pre-treatment prognostic evaluation of patients with unfavourable histology NHL

Second order gauge invariant gravitational perturbations of a Kerr black hole

We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, $\psi_I$, by explicit construction. This waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic in first order perturbations, chosen to make $\psi_I$ totally invariant and to have the appropriate behavior in an asymptotically flat gauge. $\psi_I$ fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal T}$ is the same wave operator as for first order perturbations and $S$ is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations.Comment: 19 pages, REVTEX. Some misprints corrected and changes to improve presentation. Version to appear in PR

THEORY OF PHASE-LOCKING IN SMALL JOSEPHSON JUNCTION CELLS

Within the RSJ model, we performed a theoretical analysis of phase-locking in elementary strongly coupled Josephson junction cells. For this purpose, we developed a systematic method allowing the investigation of phase-locking in cells with small but non-vanishing loop inductance.The voltages across the junctions are found to be locked with very small phase difference for almost all values of external flux. However, the general behavior of phase-locking is found to be just contrary to that according to weak coupling. In case of strong coupling there is nearly no influence of external magnetic flux on the phases, but the locking-frequency becomes flux-dependent. The influence of parameter splitting is considered as well as the effect of small capacitive shunting of the junctions. Strongly coupled cells show synchronization even for large parameter splitting. Finally, a study of the behavior under external microwave radiation shows that the frequency locking-range becomes strongly flux-dependent, whereas the locking frequency itself turns out to be flux-independent.Comment: 26 pages, REVTEX, 9 PS figures appended in uuencoded form at the end, submitted to Phys. Rev. B

Expression of topoisomerase III α in normal and neoplastic tissues determined by immunohistochemistry using novel monoclonal antibody

Topoisomerases are nuclear enzymes that modulate the topological structure of DNA in order to facilitate cellular events such as replication and transcription. These enzymes are also the cellular targets of certain classes of chemotherapeutic agents termed topoisomerase poisons. A new human topoisomerase isoform, IIIa, was discovered in 1996, which is thought to have roles in genome stability and possibly chromosome separation during mitosis. It is possible that novel or existing anti-topoisomerase agents target topoisomerase IIIa, suggesting that this enzyme may have potential as a prognostic marker and chemotherapeutic target. In order to study expression patterns of topoisomerase IIIa we have produced a novel monoclonal antibody to human topoisomerase IIIa (TOPO3a-1A4), and used it to assess topoisomerase IIIa expression in a wide range of normal and neoplastic tissues. We have found that topoisomerase IIIa is expressed in a wide range of tissue types, with especially high concentrations in endothelial cells and stromal fibroblasts. No general relationship was observed between expression of topoisomerase IIIa and proliferation. Expression in neoplastic tissues often paralleled their normal counterparts, although certain tumours showed either increased (e.g. colonic adenoma) or reduced (e.g. gastric carcinoma, small cell carcinoma of bronchus) expression. If topoisomerase IIIa is found to be a target for chemotherapeutic agents, clinical response in different tumour types may be related to topoisomerase IIIa expression, which may be assessed using TOPO3a-1A4. © 2000 Cancer Research Campaig