Centrifugal Compressor Polytropic Performance—Improved Rapid Calculation Results—Cubic Polynomial Methods

This paper presents a new improved approach to calculation of polytropic performance of centrifugal compressors. This rapid solution technique is based upon a constant efficiency, temperature-entropy polytropic path represented by cubic polynomials. New thermodynamic path slope constraints have been developed that yield highly accurate results while requiring fewer computing resources and reducing computing elapsed time. Applying this thermodynamically sound cubic polynomial model would improve accuracy and shorten compressor performance test duration at a vendor’s shop. A broad range of example case results verify the accuracy and ease of use of the method. The example cases confirm the cubic polynomial methods result in lower calculation uncertainty than other methods.

A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

A triply cubic polynomials approach for globally convergent algorithm in coefficient inverse problems

In this paper, a triply cubic polynomials approach is proposed firstly for solving the globally convergent algorithm of coefficient inverse problems in three dimension. Using Taylor type expansion for three arguments to construct tripled cubic polynomials for the approximate solution as identifying coefficient function of parabolic initial-boundary problems, in which unknown coefficients appeared at nonlinear term. The presented computational approach is effective to execute in spatial 3D issues arising in real world. Further, the complete algorithm can be straightforwardly performed to lower or higher dimensions case

O31 Trajectories of anxiety in children young people and adults with rheumatic diseases in the wake of COVID-19: results from the COVID-19 European patient registry

Background/Aims Younger and older people with rheumatic diseases may experience increased anxiety during the COVID-19 pandemic, due to the uncertainty regarding their likelihood of contracting the virus, its complications alongside their existing condition and whether their immunosuppressive treatments pose additional risks. This study explored trajectories of anxiety in parents of children and young people (CYP) with rheumatic diseases and adults with rheumatic diseases in the six months following March 2020 during the COVID-19 pandemic. Methods CYP and adults recruited to the international COVID-19 European Patient Registry, a parent-led, online, self-referred prospective cohort recruiting participants globally, were selected if enrolled within 20th March to 17th April 2020. Anxiety scores (0-10, 10=Highest anxiety) were collected weekly for up to 28 weeks and denoted parent anxiety in the CYP cohort and self-reported anxiety in the adult cohort. Group-based trajectory models explored anxiety clusters using censored-normal models in the CYP and adult populations, separately. Linear, quadratic and cubic polynomials were tested within 1 to 10 clusters and optimal models selected based on a combination of model fit (BIC), parsimony and clinical plausibility. Demographic (country, age, gender) and clinical (diagnosis, disease control, respiratory comorbidity, immunosuppressive therapy) information and COVID-19 mitigation behaviours (isolation, distancing, none) were collected at initial enrolment and compared between clusters using Chi-squared, Fisher’s exact and Kruskal-Wallis tests. Results Among 498 CYP and 2640 adults, most were female (65%, 89%) and from the UK (50%, 84%), respectively. The most common diagnoses were polyarticular JIA (37%) and oligoarticular JIA (29%) among CYP and RA among the adults (63%). Respiratory comorbidities were uncommon in the CYP (10%) and adult (17%) cohorts, and most were taking any immunosuppressive therapies (85%, 87%), respectively. As of March 2020, 88% and 79% were self-isolating, respectively. In both the parents of CYP and adult cohorts, four trajectory clusters were identified with similar patterns: Persistent extremely high anxiety (32%, 17%), persistent high anxiety (43%, 41%), high anxiety that marginally improved (25%, 32%) and moderate anxiety that improved (11%, 10%). Among CYP, few characteristics distinguished the clusters. However, in the adult cohort, clusters with greater and more persistent anxiety were associated with higher levels of respiratory comorbidities, higher use of immunosuppressive therapies, higher initial levels of self-isolation and slightly older age than those with lower or improving anxiety over time. Conclusion This study reports four trajectories of anxiety during the COVID-19 pandemic that are consistent across parents of CYP with rheumatic diseases and among adults with these conditions. Despite relatively lower risks for CYP, parental anxiety regarding COVID-19 was high and not associated with characteristics of their child or of their child's disease. Among adults with rheumatic diseases, greater anxiety was associated with risk factors potentially associated with COVID-19 morbidity and mortality. Disclosure S.J.W. Shoop-Worrall: None. S.M.M. Verstappen: None. W. Costello: None. S.P. Angevare: None. Y. Uziel: None. C. Wouters: None. N. Wulffraat: Honoraria; Sobi. Grants/research support; Abbvie. R. Beesley: None.

Malmquist-Type Theorems for Cubic Hamiltonians

The aim of this paper is to classify the cubic polynomials $$\begin{aligned} H(z,x,y)=\sum _{j+k\le 3}a_{jk}(z)x^jy^k \end{aligned}$$ H ( z , x , y ) = ∑ j + k ≤ 3 a jk ( z ) x j y k over the field of algebraic functions such that the corresponding Hamiltonian system $$x'=H_y,$$ x ′ = H y , $$y'=-H_x$$ y ′ = - H x has at least one transcendental algebroid solution. Ignoring trivial subcases, the investigations essentially lead to several non-trivial Hamiltonians which are closely related to Painlevé’s equations $$\mathrm{P_{I}}$$ P I , $$\mathrm{P_{II}}$$ P II , $$\mathrm{P_{34}}$$ P 34 , and $$\mathrm{P_{IV}}$$ P IV . Up to normalisation of the leading coefficients, common Hamiltonians are $$\begin{aligned} \begin{array}{rl} \mathrm{H_I}:&{}-2y^3+\frac{1}{2}x^2-zy\\ \mathrm{H_{II/34}}:&{} x^2y-\frac{1}{2}y^2+\frac{1}{2}zy+\kappa x\\ \mathrm{H_{IV}}:&{}\begin{array}{l} x^2y+xy^2+2zxy+2\kappa x+2\lambda y\\ \frac{1}{3}(x^3+y^3)+zxy+\kappa x+\lambda y,\end{array} \end{array} \end{aligned}$$ H I : - 2 y 3 + 1 2 x 2 - z y H II / 34 : x 2 y - 1 2 y 2 + 1 2 z y + κ x H IV : x 2 y + x y 2 + 2 z x y + 2 κ x + 2 λ y 1 3 ( x 3 + y 3 ) + z x y + κ x + λ y , but the zoo of non-equivalent Hamiltonians turns out to be much larger.