Nonharmonic transverse vibration of the H-bonded molecules and the THz spectra in ice and water

A nonlinear equation of motion is found for the dimer comprising two charged H2O molecules. The THz dielectric response to nonharmonic vibration of a nonrigid dipole, forming the hydrogen bond (HB), is found in the direction transverse to this bond. An explicit expression is derived for the autocorrelator that governs the spectrum generated by transverse vibration (TV) of such a dipole. This expression is obtained by analytical solution of the truncated set of recurrence equations. The far infrared (FIR) spectra of ice at the temperature - 7 degrees C are calculated. The wideband, in the wavenumber (frequency) v range 0... 100.0 cm(-1), spectra are obtained for liquid water at room temperature and for supercooled water at -5.6 degrees C. All spectra are represented in terms of the complex permittivity epsilon(v) and the absorption coefficient alpha(v). The obtained analytical formula for epsilon comprises the term epsilon(perpendicular to) pertinent to the studied TV mechanism with three additional terms Delta epsilon(q), Delta epsilon(mu), and epsilon(or) arising, respectively, from: elastic harmonic vibration of charged molecules along the H-bond; elastic reorientation of HB permanent dipoles; and rather free libration of permanent dipoles in 'defects' of water/ice structure. The suggested TV-dielectric relaxation mechanism allows us: (a) to remove the THz 'deficit' of loss epsilon" inherent in previous theoretical studies; (b) to explain the THz loss and absorption spectra in supercooled (SC) water; and (c) to describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H2O located in the range 10...300 cm(-1). Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of HB charged molecules. (C) 2006 Published by Elsevier B.V.

Luminous blue variables as the progenitors of supernovae with quasi-periodic radio modulations

The interaction between supernova ejecta and circumstellar matter, arising from previous episodes of mass loss, provides us with a means of constraining the progenitors of supernovae. Radio observations of a number of supernovae show quasi-periodic deviations from a strict power-law decline at late times. Although several possibilities have been put forward to explain these modulations, no single explanation has proven to be entirely satisfactory. Here we suggest that Luminous blue variables undergoing S-Doradus type variations give rise to enhanced phases of mass loss that are imprinted on the immediate environment of the exploding star as a series of density enhancements. The variations in mass loss arise from changes in the ionization balance of Fe, the dominant ion that drives the wind. With this idea, we find that both the recurrence timescale of the variability and the amplitude of the modulations are in line with the observations. Our scenario thus provides a natural, single-star explanation for the observed behaviour that is, in fact, expected on theoretical grounds.

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals, This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.

Cyclooxygenase-2 expression correlates with phaeochromocytoma malignancy.

Abstract Aims: Phaeochromocytomas are rare but potentially life-threatening neuroendocrine tumours of the adrenal medulla or sympathetic nervous system ganglia. There are no histological features which reliably differentiate benign from malignant phaeochromocytomas. The current study evaluated cyclooxygenase-2 (Cox-2) and Bcl-2 as tissue-based biomarkers of phaeochromocytoma prognosis. Methods and Results: Cox-2 and Bcl-2 expression were examined immunohistochemically in tissue from forty-one sporadic phaeochromocytoma patients followed up for a minimum of five years after diagnosis. There was a statistically significant association between Cox-2 histoscore (intensity x porportion) and the development of tumour recurrence or metastases (p=0.006). A significant relationship between the co-expression of Cox-2 and Bcl-2 in the primary tumour and the presence of recurrent disease was observed (p=0.034). A highly significant association was observed between, (i) the tumour-associated expression of these two oncoproteins (p=0.001) and, (ii) Cox-2 histoscore and the presence of Bcl-2 expression (p=0.002). Cox regression analysis demonstrated no significant relationship between, (i) the presence or absence of either Cox-2 or Bcl-2 and patient survival or, (ii) between Cox-2 histoscore and patient survival. Conclusions: These results suggest that Cox-2 and Bcl-2 may promote phaeochromocytoma malignancy and that these oncoproteins may be valuable surrogate markers of an aggressive tumour phenotype.

An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Adjusting to Life After Esophagectomy: The Experience of Survivors and Carers

Following surgery for esophageal cancer, patients can experience complex physical, social, and emotional changes. Investigation of these challenges, particularly from the perspective of the patient and his or her carer, has been limited. The current study explored the emotional and cognitive experiences of esophageal cancer survivors and those of their carers, using focus groups conducted with members of a patient support group. Analysis of the patients’ data yielded three themes: coping with a death sentence, adjusting to and accepting an altered self, and the unique benefits of peer support. Analysis of the carers’ data also yielded three themes: the carer as buffer, representations of recovery and recurrence, and normalizing experiences through peer support. Esophageal cancer patients and their carers require holistic support in their efforts to adjust to the social, emotional, and physical consequences of esophagectomy. Peers could be an effective channel for the support of patients and carers.

Bimodules over nest algebras and Deddens'

We generalise Dedden's Theorem for nest algebras to nest algebra bimodules. We define an object which extends the Jacobson radical of a nest algebra, and characterose it generalising a theorem of Erdos.

Stereotactic radiosurgery as a therapeutic strategy for intracranial metastatic prostate carcinoma.

Intracranial metastatic prostate carcinoma is rare. We sought to determine the clinical outcomes after Gamma Knife® stereotactic radiosurgery (GKSRS) for patients with intracranial prostate carcinoma metastases. We studied data from 10 patients who underwent radiosurgery for 15 intracranial metastases (9 dural-based and 6 parenchymal). Six patients had radiosurgery for solitary tumors and four had multiple tumors. The primary pathology was adenocarcinoma (eight patients) and small cell carcinoma (two patients). All patients received multimodality management for their primary tumor (including resection, radiation therapy, androgen deprivation therapy) and eight patients had evidence of systemic disease at time of radiosurgery. The mean tumor volume was 7.7 cm3 (range 1.1-17.2 cm3) and a median margin dose of 16 Gy was administered. Two patients had progressive intracranial disease in spite of fractionated partial brain radiation therapy (PBRT) prior to SRS. A local tumor control rate of 85% was achieved (including patients receiving boost, upfront and salvage SRS). New remote brain metastases developed in three patients (33%) and one patient had repeat SRS for tumor recurrence. The median survival after radiosurgery was 13 months and the 1-year survival rate was 60%. SRS was a well tolerated and effective therapy either alone or as a boost to fractionated radiation therapy in the management of patients with intracranial prostate carcinoma metastases. © 2009 Springer Science+Business Media, LLC.

Raman microscopy in the diagnosis and prognosis of surgically resected nonsmall cell lung cancer

The main curative therapy for patients with nonsmall cell lung cancer is surgery. Despite this, the survival rate is only 50%, therefore it is important to more efficiently diagnose and predict prognosis for lung cancer patients. Raman spectroscopy is useful in the diagnosis of malignant and premalignant lesions. The aim of this study is to investigate the ability of Raman microscopy to diagnose lung cancer from surgically resected tissue sections, and predict the prognosis of these patients. Tumor tissue sections from curative resections are mapped by Raman microscopy and the spectra analzsed using multivariate techniques. Spectra from the tumor samples are also compared with their outcome data to define their prognostic significance. Using principal component analysis and random forest classification, Raman microscopy differentiates malignant from normal lung tissue. Principal component analysis of 34 tumor spectra predicts early postoperative cancer recurrence with a sensitivity of 73% and specificity of 74%. Spectral analysis reveals elevated porphyrin levels in the normal samples and more DNA in the tumor samples. Raman microscopy can be a useful technique for the diagnosis and prognosis of lung cancer patients receiving surgery, and for elucidating the biochemical properties of lung tumors. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3323088]