Necessary conditions for uniqueness in L1-approximation

AbstractLet K be a compact subset of Rm with K = int K. Necessary conditions on an n-dimensional subspace Un of C(K) are given so that for each ƒ ϵ C(K) there exists a unique best L1(w)-approximation Un, for every fixed positive weight function w

Modelling lubricated revolute joints in multibody mechanical systems

This work deals with the modelling of lubricated revolute joints in multibody mechanical systems. In most machines and mechanisms, the joints are designed to operate with some lubricant fluid. The high pressures generated in the lubricant fluid act to keep the journal and the bearing apart. Moreover, the thin film formed by lubricant reduces friction and wear, provides load capacity and adds damping to dissipate undesirable mechanical vibrations. In the dynamic analysis of journal–bearings, the hydrodynamic forces, which include both squeeze and wedge effects, produced by the lubricant fluid oppose the journal motion. These forces are obtained by integrating the pressure distribution evaluated with the aid of Reynolds’ equation written for the dynamic regime. The hydrodynamic forces are nonlinear functions of journal centre position and velocity relative to the bearing centre. In a simple way, the hydrodynamic forces built up by the lubricant fluid are evaluated from the state of variable of the system and included into the equations of motion of the mechanical system. Results for an elementary slider–crank mechanism, in which a lubricated revolute joint connects the connecting rod and slider, are used to discuss the assumptions and procedures adopted.Fundação para a Ciência e a Tecnologia (FCT

Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

Eccrine porocarcinoma of the head: An important differential diagnosis in the elderly patient

Background: Eccrine porocarcinoma is a rare malignant tumor of the sweat gland, characterized by a broad spectrum of clinicopathologic presentations. Surprisingly, unlike its benign counterpart eccrine poroma, eccrine porocarcinoma is seldom found in areas with a high density of eccrine sweat glands, like the palms or soles. Instead, eccrine porocarcinoma frequently occurs on the lower extremities, trunk and abdomen, but also on the head, resembling various other skin tumors, as illustrated in the patients described herein. Observations: We report 5 cases of eccrine porocarcinoma of the head. All patients were initially diagnosed as having epidermal or melanocytic skin tumors. Only after histopathologic examination were they classified as eccrine porocarcinoma, showing features of epithelial tumors with abortive ductal differentiation. Characteristic clinical, histopathologic and immunohistochemical findings of eccrine porocarcinomas are illustrated. Conclusion: Eccrine porocarcinomas are potentially fatal adnexal malignancies, in which extensive metastatic dissemination may occur. Porocarcinomas are commonly overlooked, or misinterpreted as squamous or basal cell carcinomas as well as other common malignant and even benign skin tumors. Knowledge of the clinical pattern and histologic findings, therefore, is crucial for an early therapeutic intervention, which can reduce the risk of tumor recurrence and serious complications. Copyright (c) 2008 S. Karger AG, Basel

Lower bounds for the approximation with variation-diminishing splines

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval [0, 1] in terms of classical moduli of smoothness depending on the degree of the spline basis. For this purpose we use a functional analysis framework in order to characterize the spectrum of the Schoenberg operator and investigate the asymptotic behavior of its iterates

Oxonium ion scanning mass spectrometry for large-scale plasma glycoproteomics

Protein glycosylation, a complex and heterogeneous post-translational modification that is frequently dysregulated in disease, has been difficult to analyse at scale. Here we report a data-independent acquisition technique for the large-scale mass-spectrometric quantification of glycopeptides in plasma samples. The technique, which we named ‘OxoScan-MS’, identifies oxonium ions as glycopeptide fragments and exploits a sliding-quadrupole dimension to generate comprehensive and untargeted oxonium ion maps of precursor masses assigned to fragment ions from non-enriched plasma samples. By applying OxoScan-MS to quantify 1,002 glycopeptide features in the plasma glycoproteomes from patients with COVID-19 and healthy controls, we found that severe COVID-19 induces differential glycosylation in IgA, haptoglobin, transferrin and other disease-relevant plasma glycoproteins. OxoScan-MS may allow for the quantitative mapping of glycoproteomes at the scale of hundreds to thousands of samples

Slutsky Matrix Norms and Revealed Preference Tests of Consumer Behaviour

Given any observed finite sequence of prices, wealth and demand choices, we characterize the relation between its underlying Slutsky matrix norm (SMN) and some popular discrete revealed preference (RP) measures of departures from rationality, such as the Afriat index. We show that testing rationality in the SMN aproach with finite data is equivalent to testing it under the RP approach. We propose a way to "summarize" the departures from rationality in a systematic fashion in finite datasets. Finally, these ideas are extended to an observed demand with noise due to measurement error; we formulate an appropriate modification of the SMN approach in this case and derive closed-form asymptotic results under standard regularity conditions

Treatment of eccrine porocarcinoma with metastasis to the parotid gland using intensity-modulated radiation therapy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Cutaneous eccrine porocarcinomas are uncommon malignant tumors of the sweat gland.</p> <p>Case Presentation</p> <p>A 76-year-old Caucasian man presented to our hospital with a left temporal mass. We describe a case of eccrine porocarcinoma with metastasis to the parotid gland with special emphasis on the role of surgical resection and adjuvant radiation therapy.</p> <p>Conclusion</p> <p>Besides surgical resection, little is known about the role of adjuvant therapy in managing eccrine porocarcinomas. Radiation therapy should be considered within a multidisciplinary approach in patients with primary or recurrent eccrine porocarcinomas.</p