Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is adde

A survey of the treatment and management of patients with severe chronic spontaneous urticaria.

Chronic spontaneous urticaria (CSU) is characterized by the recurrent appearance of weals, angio‐oedema or both, occurring at least twice weekly for longer than 6 weeks.1 It is often managed with antihistamines, but occasionally requires other systemic agents in recalcitrant cases. A cross‐sectional survey was conducted by means of an internet‐based survey tool (Typeform; https://www.typeform.com). Participating consultants with a specialist interest in urticaria were identified through the specialist registers of the British Society of Allergy and Clinical Immunology (BSACI), the Improving Quality in Allergy Services (IQAS) Group and the British Association of Dermatologists (BAD), and invited to take part. The survey content was based on current CSU treatment guidelines from EAACI/GA2LEN/EDF/WAO1 and the British Society for Allergy and Clinical Immunology (BSACI).2 The EAACI/GA2LEN/EDF/WAO guidelines are a joint initiative of the Dermatology Section of the European Academy of Allergy and Clinical Immunology (EAACI), the Global Allergy and Asthma European Network (GA2LEN) (a European Union‐funded network of excellence), the European Dermatology Forum (EDF), and the World Allergy Organization (WAO). To standardize responses, all participants were presented with a case of recalcitrant CSU (failed on maximum dose of nonsedating antihistamines and montelukast), requiring alternative systemic treatment. Questions covered usage of systemic treatments, routine disease severity assessments, adherence to treatment guidelines and perceived barriers to prescribing. Responses (Table 1) were received from 19 UK consultants (26 surveys sent; completion rate 73%), 15 of whom had > 10 years’ experience in the treatment of CSU. The majority were allergy (58%) and dermatology consultants (37%). Of the 19 consultants, 56% provide a dedicated urticaria service, 37% treat both adult and paediatric patients, and the majority (79%) use systemic medications other than antihistamines and montelukast. Omalizumab and ciclosporin were the most commonly used first‐line agents (47% and 27% respectively) (Fig. 1). The majority (84%) of consultants use validated measures to assess disease severity, including the weekly Urticaria Activity Score (UAS‐7, 63%), the Physician Global Assessment (63%), the Patient Global Assessment (44%) and the Dermatology Quality of Life Index (DLQI) (38%). Guidelines are used by 89% to direct their management of CSU, with 50% using the EAACI/GA2LEN/EDF/WAO guideline,1 compared with 31% primarily using the BSACI guideline.2 The main perceived barriers to prescribing systemic medications were potential adverse effects (AEs) (32% strongly agreed), potential long‐term toxicity (26% strongly agreed), cost of treatment (42% strongly agreed), and views expressed by the patient and their family (37% agreed)

Influence of Online and Classroom Multi-modal Instruction on Academic Achievement

The purpose of the study was to investigate the extent to which online and multi-modal classroom instruction influences academic achievement of undergraduate students. Instruction was enhanced with online multimodal materials used in the face-to-face classroom presentations and for online assignments. The current study investigates not only longitudinal effectiveness in aural and visual skills learning but also possible connections among increased aural and visual skills and academic achievement measured by overall GPA.https://scholarworks.waldenu.edu/archivedposters/1094/thumbnail.jp

Extended chiral algebras in the SU(2)_0 WZNW model

We investigate the W-algebras generated by the integer dimension chiral primary operators of the SU(2)_0 WZNW model. These have a form almost identical to that found in the c=-2 model but have, in addition, an extended Kac-Moody structure. Moreover on Hamiltonian reduction these SU(2)_0 W-algebras exactly reduce to those found in c=-2. We explicitly find the free field representations for the chiral j=2 and j=3 operators which have respectively a fermionic doublet and bosonic triplet nature. The correlation functions of these operators accounts for the rational solutions of the Knizhnik-Zamolodchikov equation that we find. We explicitly compute the full algebra of the j=2 operators and find that the associativity of the algebra is only guaranteed if certain null vectors decouple from the theory. We conjecture that these algebras may produce a quasi-rational conformal field theory.Comment: 18 pages LATEX. Minor corrections. Full j=2 algebra adde

Generalized twisted modules associated to general automorphisms of a vertex operator algebra

We introduce a notion of strongly C^{\times}-graded, or equivalently, C/Z-graded generalized g-twisted V-module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V-module if V admits an additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let u be an element of V of weight 1 such that L(1)u=0. Then the exponential of 2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a strongly C-graded generalized g_{u}-twisted V-module is constructed from a strongly C-graded generalized V-module with a compatible action of g_{u} by modifying the vertex operator map for the generalized V-module using the exponential of the negative-power part of the vertex operator Y(u, x). In particular, we give examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet W-algebras. An important feature is that we have to work with generalized (twisted) V-modules which are doubly graded by the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for L(0), and the twisted vertex operators in general involve the logarithm of the formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on triplet W-algebras added, misprints corrected, and expositions revise

Vibration analysis of moving machine tool axes based on phase information in video data

Vibrations of machine tools limit quality and productivity and therefore need to be analyzed. Video based vibration analysis using spatial phase information could in principle reduce measuring effort significantly. However, feasibility of these approaches for moving machine tool axes and relative movement between camera and object is yet to be shown. This paper investigates an approach for stabilizing linear axis movement to analyze vibration. It is shown that shaker induced vibration on a linearly moving clamping tower can be derived for low frequencies. However, influences of actual cutting processes as well as compensation of unwanted camera vibration needs further investigation

Impurity intrusion in radio-frequency micro-plasma jets operated in ambient air

Space and time resolved concentrations of helium metastable atoms in an atmospheric pressure radio-frequency micro-plasma jet were measured using tunable diode laser absorption spectroscopy. Spatial profiles as well as lifetime measurements show significant influences of air entering the discharge from the front nozzle and of impurities originating from the gas supply system. Quenching of metastables was used to deduce quantitative concentrations of intruding impurities. The impurity profile along the jet axis was determined from optical emission spectroscopy as well as their dependance on the feed gas flow through the jet.Comment: Journal of Physics D: Applied Physics (accepted), 6 page

SLE local martingales in logarithmic representations

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of representations where L_0 is not diagonalizable - a phenomenon characteristic of logarithmic conformal field theory. Furthermore, we observe that the local martingales bear a close relation with the fusion product of the boundary changing fields. Our examples reproduce first of all many familiar logarithmic representations at certain rational values of the central charge. In particular we discuss the case of SLE(kappa=6) describing the exploration path in critical percolation, and its relation with the question of operator content of the appropriate conformal field theory of zero central charge. In this case one encounters logarithms in a probabilistically transparent way, through conditioning on a crossing event. But we also observe that some quite natural SLE variants exhibit logarithmic behavior at all values of kappa, thus at all central charges and not only at specific rational values.Comment: 40 pages, 7 figures. v3: completely rewritten, new title, new result

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference

Ghost Systems: A Vertex Algebra Point of View

Fermionic and bosonic ghost systems are defined each in terms of a single vertex algebra which admits a one-parameter family of conformal structures. The observation that these structures are related to each other provides a simple way to obtain character formulae for a general twisted module of a ghost system. The U(1) symmetry and its subgroups that underly the twisted modules also define an infinite set of invariant vertex subalgebras. Their structure is studied in detail from a W-algebra point of view with particular emphasis on Z_N-invariant subalgebras of the fermionic ghost system.Comment: 20 pages, plain Te