Continuous consent and dignity in dentistry

Despite the heavy emphasis on consent in the ethical code of the General Dental Council (GDC), it is often overlooked that communication difficulties between patient and dentist can cause problems in maintaining genuine consent during interventions. Inconsistencies in the GDC's Standards for dental professionals and Principles of patient consent guidelines are examined in this article, and it is concluded that more emphasis must be placed on continuous consent as an ongoing process essential to maintaining patients' dignity in dentistry

Avoidance Control on Time Scales

We consider dynamic systems on time scales under the control of two agents. One of the agents desires to keep the state of the system out of a given set regardless of the other agent's actions. Leitmann's avoidance conditions are proved to be valid for dynamic systems evolving on an arbitrary time scale.Comment: Revised edition in JOTA format. To appear in J. Optim. Theory Appl. 145 (2010), no. 3. In Pres

A Simple Theory of Condensation

A simple assumption of an emergence in gas of small atomic clusters consisting of $c$ particles each, leads to a phase separation (first order transition). It reveals itself by an emergence of ``forbidden'' density range starting at a certain temperature. Defining this latter value as the critical temperature predicts existence of an interval with anomalous heat capacity behaviour $c_p\propto\Delta T^{-1/c}$. The value $c=13$ suggested in literature yields the heat capacity exponent $\alpha=0.077$.Comment: 9 pages, 1 figur

The Wright ω Function

This paper defines the Wright ω function, and presents some of its properties. As well as being of intrinsic mathematical interest, the function has a specific interest in the context of symbolic computation and automatic reasoning with nonstandard functions. In particular, although Wright ω is a cognate of the Lambert W function, it presents a di#erent model for handling the branches and multiple values that make the properties of W difficult to work with. By choosing a form for the function that has fewer discontinuities (and numerical difficulties), we make reasoning about expressions containing such functions easier. A final point of interest is that some of the techniques used to establish the mathematical properties can themselves potentially be automated, as was discussed in a paper presented at AISC Madrid [3]

On the infrared freezing of perturbative QCD in the Minkowskian region

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [1] it is claimed that infrared freezing can be proved also for Borel resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [2]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [1]. We discuss the arguments given in [1] and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.Comment: 19 pages, 1 figur

On the chromatic roots of generalized theta graphs

The generalized theta graph \Theta_{s_1,...,s_k} consists of a pair of endvertices joined by k internally disjoint paths of lengths s_1,...,s_k \ge 1. We prove that the roots of the chromatic polynomial $pi(\Theta_{s_1,...,s_k},z) of a k-ary generalized theta graph all lie in the disc |z-1| \le [1 + o(1)] k/\log k, uniformly in the path lengths s_i. Moreover, we prove that \Theta_{2,...,2} \simeq K_{2,k} indeed has a chromatic root of modulus [1 + o(1)] k/\log k. Finally, for k \le 8 we prove that the generalized theta graph with a chromatic root that maximizes |z-1| is the one with all path lengths equal to 2; we conjecture that this holds for all k.Comment: LaTex2e, 25 pages including 2 figure

Resultant-based methods for plane curves intersection problems

http://www.springeronline.com/3-540-28966-6We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations

Optimal solutions to matrix-valued Nehari problems and related limit theorems

In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined in terms of finite dimensional restrictions of the Hankel operator. In this paper it is shown that these approximants appear as optimal solutions to restricted Nehari problems. The latter problems can be solved using relaxed commutant lifting theory. This observation is used to extent the Helton and Young approximation result to a matrix-valued setting. As in the Helton and Young paper the rate of convergence depends on the choice of the initial space in the approximation scheme.Comment: 22 page

A case of recurrent epilepsy-associated rosette-forming glioneuronal tumor with anaplastic transformation in the absence of therapy.

Rosette-forming glioneuronal tumor (RGNT) most commonly occurs adjacent to the fourth ventricle and therefore rarely presents with epilepsy. Recent reports describe RGNT occurrence in other anatomical locations with considerable morphologic and genetic overlap with the epilepsy-associated dysembryoplastic neuroepithelial tumor (DNET). Examples of RGNT or DNET with anaplastic change are rare, and typically occur in the setting of radiation treatment. We present the case of a 5-year-old girl with seizures, who underwent near total resection of a cystic temporal lobe lesion. Pathology showed morphologic and immunohistochemical features of RGNT, albeit with focally overlapping DNET-like patterns. Resections of residual or recurrent tumor were performed 1 year and 5 years after the initial resection, but no adjuvant radiation or chemotherapy was given. Ten years after the initial resection, surveillance imaging identified new and enhancing nodules, leading to another gross total resection. This specimen showed areas similar to the original tumor, but also high-grade foci with oligodendroglial morphology, increased cellularity, palisading necrosis, microvascular proliferation, and up to 13 mitotic figures per 10 high power fields. Ancillary studies the status by sequencing showed wild-type of the isocitrate dehydrogenase 1 (IDH1), IDH2, and human histone 3.3 (H3F3A) genes, and BRAF studies were negative for mutation or rearrangement. Fluorescence in situ hybridization (FISH) showed codeletion of 1p and 19q limited to the high-grade regions. By immunohistochemistry there was loss of nuclear alpha-thalassemia mental retardation syndrome, X-linked (ATRX) expression only in the high-grade region. Next-generation sequencing showed an fibroblast growth factor receptor receptor 1 (FGFR1) kinase domain internal tandem duplication in three resection specimens. ATRX mutation in the high-grade tumor was confirmed by sequencing which showed a frameshift mutation (p.R1427fs), while the apparent 1p/19q-codeletion by FISH was due to loss of chromosome arm 1p and only partial loss of 19q. Exceptional features of this case include the temporal lobe location, 1p/19q loss by FISH without true whole-arm codeletion, and anaplastic transformation associated with ATRX mutation without radiation or chemotherapy

Bubble Growth in Superfluid 3-He: The Dynamics of the Curved A-B Interface

We study the hydrodynamics of the A-B interface with finite curvature. The interface tension is shown to enhance both the transition velocity and the amplitudes of second sound. In addition, the magnetic signals emitted by the growing bubble are calculated, and the interaction between many growing bubbles is considered.Comment: 20 pages, 3 figures, LaTeX, ITP-UH 11/9