Abstract
Let H be either a complex inner product space of dimension at least two or a real inner product space of dimension at least three, and let us fix an $\alpha \in (0,\tfrac{\pi }{2} )$. The ...purpose of this paper is to characterise all bijective transformations on the projective space P(H) which preserve the quantum angle $\alpha$ (or Fubini–Study distance $\alpha$) between lines in both directions. (Let us emphasise that we do not assume anything about the preservation of other quantum angles). For real inner product spaces and when $H=\mathbb{C}^2$ we do this for every $\alpha$, and when H is a complex inner product space of dimension at least three we describe the structure of such transformations for $\alpha \leq \tfrac{\pi }{4}$. Our result immediately gives an Uhlhorn-type generalisation of Wigner’s theorem on quantum mechanical symmetry transformations, that is considered to be a cornerstone of the mathematical foundations of quantum mechanics. Namely, under the above assumptions, every bijective map on the set of pure states of a quantum mechanical system that preserves the transition probability $\cos ^2\alpha$ in both directions is a Wigner symmetry (thus automatically preserves all transition probabilities), except for the case when $H=\mathbb{C}^2$ and $\alpha = \tfrac{\pi }{4}$ where an additional possibility occurs. (Note that the classical theorem of Uhlhorn is the solution for the $\alpha = \tfrac{\pi }{2}$ case). Usually in the literature, results which are connected to Wigner’s theorem are discussed under the assumption of completeness of H; however, here we shall remove this unnecessary hypothesis in our investigation. Our main tool is a characterisation of bijective maps on unit spheres of real inner product spaces which preserve one spherical angle in both directions.
The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig’s formulation of quantum mechanics. Each effect represents a ...quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper’s first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig’s theorem. As a byproduct of our methods we also strengthen a theorem of Molnár.
Objectives
Radiosynoviorthesis (RSO) is used for the treatment of inflammatory joint diseases. However, there are no long-term results published comparing it to conservative therapy. Therefore, the ...aim of this prospective observational study was to evaluate response rates after radionuclide therapy in patients suffering from knee osteoarthritis over a time period of 10 years.
Methods
Radionuclide therapy with intra-articular administration of colloidal
90
Yttrium citrate was performed in osteoarthritic patients Kellgren–Lawrence grades I/II (
n
= 69) and Kellgren–Lawrence grade III (
n
= 72).
Results
In patients with early-stage disease, an excellent/good response with respect to pain, joint mobility, and function was observed in 82.5% for 1 year and in 73.7% for 8 years after therapy. Responses declined to 50% at 10 years post treatment. In grade III patients, an excellent/good response was observed in 45.9%; a decline to 41.2% was observed in the first 8 years. In this group, the number of patients available for follow-up after 9 and 10 years dropped significantly from 51 patients after 8 years to only 30 patients after 9 years, and to nine patients after 10 years. As a result, these response rates were not appraisable.
Conclusion
Long-term results of radiosynoviorthesis in knee osteoarthritis are excellent/good in many patients. The response rate depends on Kellgren–Lawrence stages, and early-stage radionuclide therapy for osteoarthritis is suggested.
To assess (A) determinants of patient's global assessment of disease activity (PTGL) and patient's assessment of general health (GH) scores of rheumatoid arthritis (RA) patients; (B) whether they are ...equivalent as individual variables; and (C) whether they may be used interchangeably in calculating common RA activity assessment composite indices.
Data of 7023 patients from 30 countries in the Quantitative Standard Monitoring of Patients with RA (QUEST-RA) was analysed. PTGL and GH determinants were assessed by mixed-effects analyses of covariance models. PTGL and GH equivalence was determined by Bland-Altman 95% limits of agreement (BALOA) and Lin's coefficient of concordance (LCC). Concordance between PTGL and GH based Disease Activity Score 28 (DAS28), Clinical Disease Activity Index (CDAI) and Routine Assessment of Patient Index Data 3 (RAPID3) indices were calculated using LCC, and the level of agreement in classifying RA activity in four states (remission, low, moderate, high) using κ statistics.
Significant differences in relative and absolute contribution of RA and non-RA related variables in PTGL and GH ratings were noted. LCC of 0.64 and BALOA of -4.41 to 4.54 showed that PTGL and GH are not equivalent. There was excellent concordance (LCC 0.95-0.99) for PTGL and GH based DAS28, CDAI and RAPID3 indices, and >80% absolute agreement (κ statistics 0.75-0.84) in RA activity state classification for all three indices.
PTGL and GH ratings differ in their determinants. Although they are individually not equivalent, they may be used interchangeably for calculating composite indices for RA activity assessment.
Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of ...a complex Hilbert space which preserves the transition probability is induced by a unitary or an antiunitary operator. This vital theorem has been generalised in various ways by several scientists. In 2001, Molnár provided a natural generalisation, namely, he provided a characterisation of (not necessarily bijective) maps which act on the Grassmann space of all rank-n projections and leave the system of Jordan principal angles invariant (see 17 and 20). In this paper we give a very natural joint generalisation of Wigner's and Molnár's theorems, namely, we prove a characterisation of all (not necessarily bijective) transformations on the Grassmann space which fix the quantity TrPQ (i.e. the sum of the squares of cosines of principal angles) for every pair of rank-n projections P and Q.
PT2-1 EBM Balneotherapy in Hungary BENDER, Tamas; BÁLINT, Géza; GÉHER, Pál ...
The Journal of The Japanese Society of Balneology, Climatology and Physical Medicine,
2014, Letnik:
77, Številka:
5
Journal Article
Odprti dostop
Hungary is rich in thermal mineral waters. Here, we present a systematic review and meta-analysis of clinical trials conducted with Hungarian thermal mineral waters, the findings of which have been ...published by Hungarian authors in English. The 124 studies identified in different databases include 20 clinical trials. Seven of these evaluated the effect of hydro- and balneotherapy on chronic low back pain, four on osteoarthritis of the knee, and two on osteoarthritis of the hand and one ostheoarthrtis of shoulder. One of the remaining seven trials evaluated balneotherapy in chronic inflammatory pelvic diseases, while six studies explored its effect on various laboratory parameters. Out of the 20 studies, 9 met the predefined criteria for meta-analysis.The results confirmed the beneficial effect of balneotherapy on pain with weightbearing and at rest in patients with degenerative joint and spinal diseases. A similar effect has been found in chronic pelvic inflammatory disease. The review also revealed that balneotherapy has some beneficial effects on antioxidant status, and on metabolic and inflammatory parameters.Based on the results, we conclude that balneotherapy with Hungarian thermal-mineral waters is an effective remedy for lower back pain, as well as for knee and hand and shoulder osteoarthritis.
To update the Assessment of SpondyloArthritis international Society (ASAS)-EULAR recommendations for the management of axial spondyloarthritis (axSpA).
Following the EULAR Standardised Operating ...Procedures, two systematic literature reviews were conducted on non-pharmacological and pharmacological treatment of axSpA. In a task force meeting, the evidence was presented, discussed, and overarching principles and recommendations were updated, followed by voting.
Five overarching principles and 15 recommendations with a focus on personalised medicine were agreed: eight remained unchanged from the previous recommendations; three with minor edits on nomenclature; two with relevant updates (#9, 12); two newly formulated (#10, 11). The first five recommendations focus on treatment target and monitoring, non-pharmacological management and non-steroidal anti-inflammatory drugs (NSAIDs) as first-choice pharmacological treatment. Recommendations 6-8 deal with analgesics and discourage long-term glucocorticoids and conventional synthetic disease-modifying antirheumatic drugs (DMARDs) for pure axial involvement. Recommendation 9 describes the indication of biological DMARDs (bDMARDs, that is, tumour necrosis factor inhibitors (TNFi), interleukin-17 inhibitors (IL-17i)) and targeted synthetic DMARDs (tsDMARDs, ie, Janus kinase inhibitors) for patients who have Ankylosing Spondylitis Disease Activity Score ≥2.1 and failed ≥2 NSAIDs and also have either elevated C reactive protein, MRI inflammation of sacroiliac joints or radiographic sacroiliitis. Current practice is to start a TNFi or IL-17i. Recommendation 10 addresses extramusculoskeletal manifestations with TNF monoclonal antibodies preferred for recurrent uveitis or inflammatory bowel disease, and IL-17i for significant psoriasis. Treatment failure should prompt re-evaluation of the diagnosis and consideration of the presence of comorbidities (#11). If active axSpA is confirmed, switching to another b/tsDMARD is recommended (#12). Tapering, rather than immediate discontinuation of a bDMARD, can be considered in patients in sustained remission (#13). The last recommendations (#14, 15) deal with surgery and spinal fractures.
The 2022 ASAS-EULAR recommendations provide up-to-date guidance on the management of patients with axSpA.
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