Archimedes Force on Casimir Apparatus

We address a problem of Casimir apparatus in dense medium and weak gravitational field. The falling of the apparatus has to be governed by the equivalence principle, with proper account for contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general expression for the corresponding force in metric with cylindrical symmetry. By way of example we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.Comment: 13 pages, 1 figur

Lattice isomorphisms of bisimple monogenic orthodox semigroups

Using the classification and description of the structure of bisimple monogenic orthodox semigroups obtained in \cite{key10}, we prove that every bisimple orthodox semigroup generated by a pair of mutually inverse elements of infinite order is strongly determined by the lattice of its subsemigroups in the class of all semigroups. This theorem substantially extends an earlier result of \cite{key25} stating that the bicyclic semigroup is strongly lattice determined.Comment: Semigroup Forum (published online: 15 April 2011

Modular and lower-modular elements of lattices of semigroup varieties

The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the variety COM of all commutative semigroups or a nil-variety or the join of a nil-variety with the variety of semilattices. Second, we prove that if a commutative nil-variety is a modular element of Com then it may be given within COM by 0-reduced and substitutive identities only. Third, we completely classify all lower-modular elements of Com. As a corollary, we prove that an element of Com is modular whenever it is lower-modular. All these results are precise analogues of results concerning modular and lower-modular elements of the lattice of all semigroup varieties obtained earlier by Jezek, McKenzie, Vernikov, and the author. As an application of a technique developed in this paper, we provide new proofs of the `prototypes' of the first and the third our results.Comment: 15 page

Howard Shevrin on Peter Wolff

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68168/2/10.1177_00030651990470011701.pd

Generalized Green'S Equivalences on the Subsemigroups of the Bicyclic Monoid

We study generalized Green's equivalences on all subsemigroups of the bicyclic monoid B and determine the abundant (and adequate) subsemigroups of B. © 2010 Copyright Taylor and Francis Group, LLC

Commentaries

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66660/2/10.1177_00030651970450031209.pd

Role-Clarity and Boundaries for Trauma-Informed Teachers

As they begin to implement trauma-informed practices in their classrooms, teachers should consider their role in the lives of students and how to maintain appropriate and safe boundaries with students. This essay explores the role of the teacher in supporting trauma-affected children and offers a frame of teacher as a facilitator of connection. It also offers ways to compassionately maintain boundaries with students while supporting their access to mental health care

Event-related potential indicators of the dynamic unconscious

The present study applies a new method for investigating dynamic unconscious processes. The method consists of (1) selection of words from patient interview and test protocols that in the clinicians' judgments capture the patients' conscious symptom experience (i.e. [phobia) and the hypothetical unconscious conflict related to the symptom, (2) subliminal and supraliminal presentation of these words, (3) signal analysis of event-related potentials (ERPs) obtained to the word presentations. Eight phobics and three patients suffering from pathological grief reactions served as subjects. A time-frequency (Williams & Joeng, 1989) ERP analysis revealed that subjects' ERPs classified the unconscious conflict words better subliminally than supraliminally, while the reverse was true for the conscious symptom words (t(20) = 2.82, P = .011). The relationship between frequency and latency revealed a similar mirror image pattern for the unconscious conflict and conscious symptom words (F(4/36) = 4.14, P = .007). This method demonstrated that objective, brain-based evidence for unconscious conflict can be obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29875/1/0000225.pd

Semigroups with certain finiteness conditions and Chernikov groups

The main purpose of this short survey is to show how groups of special structure, which are accepted to be called Chernikov groups, appeared in the considerations of semigroups with certain finiteness conditions. A structure of groups with several such conditions has been described (they turned out to be special types of Chernikov groups). Lastly, a question concerning some special type of Chernikov groups is recalled; this question was raised by the author more than 35 years ago, and it is still open