1,721,211 research outputs found
On the Resolution of Third and Fourth Degree Equations
No full textIn this paper we deal with the resolution of third and fourth degree equations by means of radicals. We present some historical details about this fundamental problem. We also discuss practical methods for the resolution of third and fourth degree equations from the algebraic point of view. Finally, we introduce some results about the equations of greater degree
Wine and maths: mathematical solutions to wine–inspired problems
No full textWe deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth z0 of a wine cellar in order to attenuate the periodic temperature fluctuations. What follows is a kind of survey of wine-related and optimization problems which have been solved by means of powerful math tools
Weak-Type Estimates for the Metaplectic Representation Restricted to the Shearing and Dilation Subgroup of SL(2,R)
Full text linkWe consider the subgroup G of SL(2, R) consisting of shearing and dilations, and we study the decay at infinity of the matrix coefficients of the metaplectic representation restricted to G. We prove weak-type estimates for such coefficients, which are uniform for functions in the modulation space M 1 . This work represents a continuation of a project aiming at studying weak-type and Strichartz estimates for unitary representations of non-compact Lie groups
Strichartz estimates for the metaplectic representation
Full text linkWe provide new estimates for the matrix coefficients of the metaplectic representation, inspired by a formal analogy with the Strichartz estimates which hold for several classes of evolution propagators U(t). The one parameter group of unitary operators U(t) is replaced by a unitary representation of a non-compact Lie group, the group element playing the role of time; the case of the metaplectic or oscillatory representation is of special interest in this connection, because the Schroedinger group is a subgroup of the metaplectic group. We prove uniform weak-type sharp estimates for matrix coefficients and Strichartz-type estimates for that representation. The crucial point is the choice of function spaces able to detect such a decay, which in general will depend on the given group action. The relevant function spaces here turn out to be the so-called modulation spaces from Time-frequency Analysis in Euclidean space, and Lebesgue spaces with respect to Haar measure on the metaplectic group. The proofs make use in an essential way of the covariance of the Wigner distribution with respect to the metaplectic representation
Wine and maths: mathematical solutions to wine–inspired problems
No full textWe deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth z0 of a wine cellar in order to attenuate the periodic temperature fluctuations. What follows is a kind of survey of wine-related and optimization problems which have been solved by means of powerful math tools
Psoriatic Arthritis and Outcome Measures
No full textFil: Cauli, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Porru, G. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Piga, M. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Vacca, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; ItalyFil: Mathieu, A. University of Cagliari. Department of Medical Sciences. Rheumatology Unit; Ital
Treatment of Facet Joints
No full textLumbar zygapophysial joints are also called “facet joints” They are often cause of chronic back pain because of rich innervation of the articular structures. In 1933, Ghormley named the spectrum of symptoms arising from its pathological involvement as “facet joint syndrome” (FCS).FCS represents 15% of chronic pain in the lower back. It is characterized by joint pain which is usually insidious in its onset and which may derive from almost any structure in the zygapophysial joints (fibrous capsule, synovial membrane, hyaline cartilage, tendons, bone) due to mechanical or inflammatory stimulation of nociceptors. Standard treatments for pain in lumbar facet joints are mainly intra-articular injections of corticosteroids and radiofrequency denervation (RFD) of the medial branches which innervate the zygapophysial joint. We review here the anatomy and physiology of the lumbar zygapophysial joints as well as diagnostic tools and treatments
[Quantification of cellular antigens by means of flow cytometry and its role in rheumatology]
No full textFlow cytometric analysis is a technique which allows not only phenotypical characterization of cellular subsets but also allows quantitation of cellular antigens. In this paper we summarize the Molecules of Equivalent Soluble Fluorochromes (MESF) units and the Antibody Binding Capacity (ABC) methods
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