The N = 1 super Heisenberg–Virasoro vertex algebra at level zero

We study the representation theory of the [Formula: see text] super Heisenberg–Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342; D. Adamović and G. Radobolja, Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math. 21(2) (2019) 1850008; Y. Billig, Representations of the twisted Heisenberg–Virasoro algebra at level zero, Can. Math. Bull. 46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On W-algebras associated to [Formula: see text] minimal models and their representations, Int. Math. Res. Notices 2010(20) (2010) 3896–3934].

Effects of isentropic efficiency of turbomachinery components on entropy production for small turbojet engine

Purpose Usage of gas turbine engines has increased by day due to rising demand for military and civil applications. This case results in investigating diverse topics related to energy efficiency and irreversibility of these systems. The purpose of this paper is to perform a detailed entropy assessment of turbojet engines for different flight conditions. Design/methodology/approach In this study, for small turbojet engines used in unmanned aerial vehicles, parametric cycle analysis is carried out at (sea level-zero Mach (hereinafter phase-I)) and (altitude of 9,000 m- Mach of 0.7 (hereinafter phase-II)). Based on this analysis, variation of performance and thermodynamic parameters with respect to change in isentropic efficiency of the compressor (CIE) and turbine (TIE) is examined at both phases. In this context, the examined ranges for CIE is between 0.78 and 0.88 whereas TIE is between 0.85 and 0.95. Findings Increasing isentropic efficiency decreases entropy production of the small turbojet engine. Moreover, the highest entropy production occurs in the combustor in the comparison of other components. Namely, it decreases from 2.81 to 2.69 kW/K at phase-I and decreases from 1.44 to 1.39 kW/K at phase-II owing to rising CIE. Practical implications It is thought that this study helps in understanding the relationship between entropy production and the efficiency of components. Namely, the approach used in the current analysis could help decision-makers or designers to determine the optimum value of design variables. Originality/value Due to rising isentropic efficiencies of both components, it is observed that specific fuel consumption (SFC) decreases whereas specific thrust (ST) increases. Also, the isentropic efficiency of a compressor affects relatively SFC and ST higher than that of the turbine.

Construct Validity of a Fascism Scale with Comparison to Ethnonationalism

The current study involves construct validation of a questionnaire developed by Saucier (2013) that measures fascist beliefs as theorized by Robert Paxton (2007), construing them as mobilizing passions. We distinguished fascist beliefs from ethnonationalism, another extreme political attitude associated with campaigns of genocide and ethnic cleansing. We conducted principal components analysis on both the fascism and ethnonationalism scales to assess dimensionality, finding that individual differences in a theoretically grounded construct of fascism can be coherently measured by a relatively brief set of items. The results of item analysis on the fascism scale generated two even briefer fascism scales to be compared in future studies. We examined item-level zero-order correlations to assess the relation between the constructs and found moderate overlap but not redundancy between the constructs of Paxtonian fascism and ethnonationalism, suggesting that they should be treated as discrete sets of beliefs. The construction of the Paxtonian fascism scale offers a first step towards accounting for the role of fascism in predicting campaigns of genocide and ethnic cleansing and other forms of political violence.

Base change for ramified unitary groups: The strongly ramified case

We compute a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. In this special case, we require the given supercuspidal representation to contain a skew maximal simple stratum, and the field datum of this stratum to be of maximal degree, tamely ramified over the base field, and quadratic ramified over its subfield fixed by the Galois involution that defines the unitary group. The base change of this supercuspidal representation is described by a canonical lifting of its underlying simple character, together with the base change of the level-zero component of its inducing cuspidal type, modified by a sign attached to a quadratic Gauss sum defined by the internal structure of the simple character. To obtain this result, we study the reducibility points of a parabolic induction and the corresponding module over the affine Hecke algebra, defined by the covering type over the product of types of the given supercuspidal representation and of a candidate of its base change.