Massless spin 3/2 field, spherical solutions, eliminating of the gauge degrees of freedom

Relativistic system for a vector-bispinior describing a massless spin 3/2 field is studied in the spherical coordinates of Minkowski space. Presentation of the equation with the use of the covariant Levi-Civita tensor exhibits existence of the gauge solutions in the form of the covariant 4-gradient of an arbitrary bispinor. Substitution for 16-component field function is based on the use of Wigner functions, it assumes diagonalization of the operators of energy, square and third projection of the total angular momentum, and space reflection. We derive radial system for eight independent functions. General structure of the spherical gauge solutions is specified, and it is demonstrated that the gauge radial functions satisfy the derived system. It is proved that the general system reduces to two couples of independent 2-nd order and nonhomogeneous differential equations, their particular solutions may be found with the use of the gauge solutions. The corresponding homogeneous equations have one the same form, they have three regular singularities and one irregular of the rank 2. Frobenius types solutions for this equation have been constructed, and the structure of the involved power series with 4-term recurrent relations sre studied. Six remaining radial functions may be straightforwardly found by means of the simple algebraic relations. Thus, we have constructed two types of solutions with opposite parities which do not contain gauge constituents.

Sistem Pendukung Keputusan Pemilihan Kain Terbaik Di Toko Crown Textile & Tailor Dengan Metode Simple Additive Weighting (SAW)

The retail business continues to grow rapidly along with the development of science and technology in the era of globalization, but the purchase of fabric is still done manually and not computerized, such as in choosing fabrics, only looking at the shape of the color and the price tag, if it is suitable and likes it is taken immediately without thinking what type of fabric to use. used for these clothes, when they have been made into clothes or clothes, do not match the criteria desired by consumers and many ready-made clothes are returned because the color becomes dull or faded, and does not match the desired motif. The problem in this study is to determine the selection of the best fabric using SPK with the Simple Additive Weighting (SAW) method in selecting the best fabric at Crown Textile Tailor built using PHP MyAdamin programming. The decision support system method used is Simple Additive Weighting (SAW), because it can determine the weight value for each attribute, through a ranking process selecting the best alternative from a number of alternative data, the results obtained are Viscose Rayon Fabrics worth 0.933, (Rank 1), Brukat Lace Fabrics are worth 0 .9 (Rank 2), Toyobo Cotton Fabric is worth 0.716 (Rank 3), Japanese Cotton Fabric is worth 0.700 (Rank 4).

Automorphisms and Some Geodesic Properties of Ortho-Grassmann Graphs

Let $H$ be a complex Hilbert space. Consider the ortho-Grassmann graph $\Gamma^{\perp}_{k}(H)$ whose vertices are $k$-dimensional subspaces of $H$ (projections of rank $k$) and two subspaces are connected by an edge in this graph if they are compatible and adjacent (the corresponding rank-$k$ projections commute and their difference is an operator of rank $2$). Our main result is the following: if $\dim H\ne 2k$, then every automorphism of $\Gamma^{\perp}_{k}(H)$ is induced by a unitary or anti-unitary operator; if $\dim H=2k\ge 6$, then every automorphism of $\Gamma^{\perp}_{k}(H)$ is induced by a unitary or anti-unitary operator or it is the composition of such an automorphism and the orthocomplementary map. For the case when $\dim H=2k=4$ the statement fails. To prove this statement we compare geodesics of length two in ortho-Grassmann graphs and characterise compatibility (commutativity) in terms of geodesics in Grassmann and ortho-Grassmann graphs. At the end, we extend this result on generalised ortho-Grassmann graphs associated to conjugacy classes of finite-rank self-adjoint operators.

Hamiltonian analysis and positivity of a newmassive spin-2 model

Recently a new model has been proposed to describe free massive spin-2 particles in D dimensions in terms of a non symmetric rank-2 tensor eµν and a mixed symmetry tensor Bµ[αβ]. The model is invariant under linearized diffeomorphisms without Stueckelberg fields. It resembles a spin-2 version of the topologically massive spin-1 BF model (Cremmer-Scherk model). Here we apply the Dirac-Bergmann procedure in order to identify all Hamiltonian constraints and perform a complete counting of degrees of freedom. In D = 3 + 1 we find 5 degrees of freedom corresponding to helicities ±2, ±1, 0 as expected. The positivity of the reduced Hamiltonian is proved by using spin projection operators. We have also proposed a parent action that establishes the duality between the Fierz-Pauli and the new model. The equivalence between gauge invariant correlation functions of both theories is demonstrated.

The Axiomatics of Free Group Rings

In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined. Here we assume that $R$ is a commutative ring with identity $1 \ne 0$. Of course, these are relative to an appropriate logical language $L_0,L_1,L_2$ for groups, rings and group rings respectively. Axiom systems for these were provided in [FGRS1]. In [FGRS1] it was proved that if $R[G]$ is elementarily equivalent to $S[H]$ with respect to $L_{2}$, then simultaneously the group $G$ is elementarily equivalent to the group $H$ with respect to $L_{0}$, and the ring $R$ is elementarily equivalent to the ring $S$ with respect to $L_{1}$. We then let $F$ be a rank $2$ free group and $\mathbb{Z}$ be the ring of integers. Examining the universal theory of the free group ring ${\mathbb Z}[F]$ the hazy conjecture was made that the universal sentences true in ${\mathbb Z}[F]$ are precisely the universal sentences true in $F$ modified appropriately for group ring theory and the converse that the universal sentences true in $F$ are the universal sentences true in ${\mathbb Z}[F]$ modified appropriately for group theory. In this paper we show this conjecture to be true in terms of axiom systems for ${\mathbb Z}[F]$.

Accuracy of single intravenous access iohexol GFR in children is hampered by marker contamination

Measurement of glomerular filtration rate (GFR) in children by iohexol injection and blood sampling from the contralateral arm is widely used. A single intravenous access for iohexol injection and subsequent blood sampling has the obvious advantages of being less painful and easier to perform. The purpose of our study was to determine if blood samples drawn from the injection access are feasible and accurate for iohexol GFR (iGFR) measurements. Thirty-one children, median age 10.5 (range 6–17) years, with chronic kidney disease were given a bolus of iohexol followed by extended saline flushing and subsequent venous blood samples collected from the injection access as well as from a cannula in the contralateral arm, the latter serving as the reference method. Paired venous blood samples were collected at four time points (2, 3, 3.5 and 4 h) after the iohexol bolus. Blood sample discarding preceded and saline flushing followed each blood sampling to avoid marker contamination. iGFR based on samples drawn from the injection access at 2 and 3 h showed significantly lower iGFR than measurement from the contralateral arm (p < 0.01). Singlepoint iGFR did not differ significantly after 3–4 repeated procedures of blood discarding and saline flusing (3.5 and 4 h). Despite thorough saline flushing there is still a relatively high risk of falsely low iGFR due to marker contamination in blood samples from the injection site. Hence, blood sampling from a second intravenous access is recommended for routine iohexol GFR measurements in children.Clinical trial registration: ClinicalTrials.gov, Identifier NCT01092260, https://clinicaltrials.gov/ct2/show/NCT01092260?term=tondel&rank=2.

Critical issue on the extinction and inattention subtest of NIHSS scale: an analysis on post-acute stroke patients attending inpatient rehabilitation

Objectives This study aims to evaluate the diagnostic performance of NIHSS extinction and inattention item, compared to the results of the Oxford Cognitive Screen (OCS) heart subtest. Additionally, the possible role of the NIHSS visual field subtest on the NIHSS extinction and inattention subtest performance is explored and discussed. Methods We analysed scores on NIHSS extinction and inattention subtest, NIHSS visual field subtest, and OCS heart subtest on a sample of 118 post-stroke patients. Results Compared to OCS heart subtest, the results on NIHSS extinction and inattention subtest showed an accuracy of 72.9% and a moderate agreement level (Cohen’s kappa = 0.404). Furthermore, a decrease in NIHSS accuracy detecting neglect (61.1%) was observed in patients with pathological scores in NIHSS visual field item. Conclusions Extreme caution is recommended for the diagnostic performance of extinction and inattention item of NIHSS. Signs of neglect may not be detected by NIHSS, and may be confused with visual field impairment. Trial registration This study refers to an observational study protocol submitted to ClinicalTrials.gov with identifier: NCT03968627. The name of the registry is “Development of a National Protocol for Stroke Rehabilitation in a Multicenter Italian Institution” and the date of the registration is the 30th May 2019.

One-loop partition function, gauge accessibility and spectra in AdS3 gravity

We continue the study of the one-loop partition function of AdS3 gravity with focus on the square-integrability condition on the fluctuating fields. In a previous work we found that the Brown-Henneaux boundary conditions follow directly from the L2 condition. Here we rederive the partition function as a ratio of Laplacian determinants by performing a suitable decomposition of the metric fluctuations. We pay special attention to the asymptotics of the fields appearing in the partition function. We also show that in the usual computation using ghost fields for the de Donder gauge, such gauge condition is accessible precisely for square-integrable ghost fields. Finally, we compute the spectrum of the relevant Laplacians in thermal AdS3, in particular noticing that there are no isolated eigenvalues, only essential spectrum. This last result supports the analytic continuation approach of David, Gaberdiel and Gopakumar. The purely essential spectra found are consistent with the independent results of Lee and Delay of the essential spectrum of the TT rank-2 tensor Lichnerowickz Laplacian on asymptotically hyperbolic spaces.