Richardson Criterion Research Articles

Managing massive palatial defect secondary to palatoplasty failures: an in-depth analysis.

Massive palatal defects resulting from palatoplasty failures arising from cleft palate repair complications present ongoing challenges in clinical practice. The purpose of this review is to provide up-to-date insights into aetiology, risk factors, surgical techniques, and adjunctive therapies, aiming to enhance the understanding of such complex cases, and optimize patient outcomes. Primary palatoplasty has fistula recurrence rates ranging from 2.4% to 55%. Factors such as cleft width, surgical repair method, and patient characteristics, influence the likelihood of failure. Classifications such as the Pakistan Comprehensive Classification and Richardson's criteria aid in assessing defects. Surgical options range from local flaps and revision palatoplasty to regional flaps (e.g., buccinator myomucosal, facial artery-based flaps, tongue flaps, nasal septal flaps) to free microvascular flaps. Alternative approaches include obturator prostheses, and acellular dermal matrix has been used as an adjuvant to multiple repair techniques. Hyperbaric oxygen therapy has emerged as an adjunctive therapy to enhance tissue healing. This comprehensive review underscores the intricate challenges associated with massive palatal defects resulting from palatoplasty failures. The diverse range of surgical and nonsurgical options emphasizes the importance of patient-centric, individualized approaches. Practitioners, armed with evidence-based insights, can navigate these complexities, offering tailored interventions for improved patient outcomes.

Evaluation of Number Density of Tumor-Associated Macrophages by Immunohistochemistry and Semiquantitative Scoring in Invasive Breast Cancer: An Indian Study.

Tumor microenvironment is emerging as a critical factor for progression of breast cancer. Tumor-associated macrophages (TAMs) play an important role in promoting tumor growth. This study was aimed at correlation of number density (ND) of TAMs with invasive ductal carcinoma (IDC) grading utilizing an image morphometric technique. We also sought to compare the TAMs and ND in the tumoral area and stromal region. We also explored the relationship between the clinical and pathological prognostic parameters. The study included 75 cases of IDC that had undergone modified radical mastectomy. The Institutional Ethics Committee approved the study. Samples were classified as Grade 1, 2, and 3. Cases were graded as per the modified Bloom and Richardson criterion. Mean with standard deviation was calculated for each group. We utilized CD68 and CD163 immunostained sections for determining the ND of TAMs. TAMs were evaluated using computerized digital photomicrograph system with image analyzing software. ND was defined as the number of TAMs in total number of TAMs in five high-power fields/total area of five fields. ND was calculated separately in tumor and tumor stroma (TS). Estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2/neu (HER2/neu) were scored in accordance with recommendations. Ki-67 was scored as per the recommended guidelines. Data were tabulated in Microsoft Excel. SPSS version 20.0 (IBM Corp., Armonk, NY, USA) was used for statistical analysis. To determine the relationship between macrophage density and clinicopathologic parameters, we used the independent t-test. To determine the differences in the parameters, analysis of variance (ANOVA) was utilized. Age of the patients ranged from 34 to 58 years (mean: 55.5). One-way ANOVA between various grades of tumor indicating significant differences in terms of CD68 and CD163 densities in tumor and stroma (P < 0.0001). i.e., significant increased density of CD68 and CD163 was observed in Grade 3 tumor as compared to other two groups. A greater histological grade, ER, PR negative status, and a high Ki-67 index were all associated with TAM ND. There was no relation to HER2/neu status. Result of unpaired t-test indicates increased density in stroma as compared to tumor among various grades of IDC. We analyzed images with a software using photographs of the stained slides. This helped in quantitative analysis of TAMs on the CD68 and CD163 stained sections. This approach standardizes and reproducibly counts TAMs per unit area. We found significant difference between the number densities of TAMs in grades of invasive breast carcinoma. There were statistically significant differences in numerical densities of TAMs with ER, PR negativity, and Ki-67. There was no correlation with HER2/neu. Densities of CD68 and CD163 densities are more prevalent in TS as compared to intratumoral region.

Revisiting Sayers: One Hundred Years of Canons of Classification

William Charles Berwick Sayers (1881-1960), an English librarian, made outstanding contributions to the development of a theory of library classification. He is referred to as the first grammarian of library classification. Even though he did not design any classification scheme, he interpreted and systematised the ideas of other theoreticians to formulate guidelines for designing library classification schemes. Sayers presented his theory of classification by stating 29 principles, called Canons, in 1915. He desired to make a comparative study of his canons with Richardson's Criteria, Bliss' Principles and Ranganathan's Canons. This paper presents a comparative study of Sayers' Canons (29 Canons), Bliss' Principles (32 Principles) and Ranganathan's Canons (43 Canons). Richardson stated only five Criteria in the form of general instructional statements these are not included in this study. Sayers' two Canons are similar to both Bliss' Principles and Ranganathan's Canons. Bliss' three Principles show highest similarity with Sayers' five Canons. Ranganathan's three Canons show highest similarity with Sayers' Canons, which are Canon of Currency (Verbal plane), Canon of Reticence (Verbal plane) and Canon of Hierarchy (Notational plane) respectively.

Physics of tidal dissipation in early-type stars and white dwarfs: hydrodynamical simulations of internal gravity wave breaking in stellar envelopes

ABSTRACT In binaries composed of either early-type stars or white dwarfs, the dominant tidal process involves the excitation of internal gravity waves (IGWs), which propagate towards the stellar surface, and their dissipation via non-linear wave breaking. We perform 2D hydrodynamical simulations of this wave breaking process in a stratified, isothermal atmosphere. We find that, after an initial transient phase, the dissipation of the IGWs naturally generates a sharp critical layer, separating the lower stationary region (with no mean flow) and the upper ‘synchronized’ region (with the mean flow velocity equal to the horizontal wave phase speed). While the critical layer is steepened by absorption of these waves, it is simultaneously broadened by Kelvin–Helmholtz instabilities such that, in steady state, the critical layer width is determined by the Richardson criterion. We study the absorption and reflection of incident waves off the critical layer and provide analytical formulae describing its long-term evolution. The result of this study is important for characterizing the evolution of tidally heated white dwarfs and other binary stars.

The Peculiarities of Convective Heat Transfer in Melt of a Multiple-Electrode Arc Furnace

The modern direction of improving the technology of steel production in high-power arc furnaces is the intensification of magnetohydrodynamic effects for mixing the melt. In this article, a furnace design is proposed that contains three roof arc and three bottom electrodes, which provides the formation of additional eddy currents in the melt when the furnace is supplied with direct current or a low-frequency current. For a numerical study of the features of heat transfer in the melt of this furnace, a three-dimensional mathematical model of magnetohydrodynamic and thermal processes was used. The results were processed using the methods of visualization of vortex structures and the Richardson criterion. In an oven with a capacity of 180 tons at currents in the electrodes of 80 kA, the conditions for the interaction of electric vortex and thermogravitational convection were studied. Results showed that thermogravitational convection due to nonuniform heating of the melt led to a decrease in the size of the main electric vortex flow and the formation of an additional flow near the side walls of the furnace. The features of azimuthal flows formed in the areas of electric arcs and hearth electrodes were analyzed. Results showed that the multivortex structure of the flows that formed in the furnace allowed the volume of stagnant zones to be reduced and provided acceptable melt mixing conditions. The results can be used to improve the energy and structural parameters of three-electrode arc furnaces.

Viscous stress tensor and stability of laminar contravortical flows

Introduction: coaxial layers in contravortical flows rotate in the opposite directions. This determines their complicated spatial structure. The relevance of the subject is in the uniquely effective mixing of the moving medium. This property has a great potential of application from microbiology and missile building for obtaining highly dispersed mixtures to heat engineering for increasing the intensity of heat transfer. However, contravortical flows have a high degree of hydrodynamic instability. This hinders effective development of these technologies. Contravortical flows are observed behind Francis hydroturbines, whose derated operation causes modes with a significant increase of hydraulic unit vibrations up to destruction of the units. The purpose of the study is to identify physical laws of the contravortical flow hydrodynamics, common for both laminar and turbulent fluid flow modes.&#x0D; Materials and methods: theoretical analysis of the viscous stress tensor and local stability zones of contravortical laminar flows.&#x0D; Results: the article provides a mathematical description of the tensor of viscous tangential (τij) and normal (σii) stresses as well as local stability zones of the flow according to Rayleigh (Ra) and Richardson (Ri) criteria. The graphs of the radial-axial distributions of the viscous stress components are given, local stability zones are shown and the point of “vortex breakdown” is indicated. The solutions are obtained in the form of Fourier – Bessel series. The hydrodynamic structure of the flow is analysed.&#x0D; Conclusions: it is established that the most significant viscous stresses are observed at the beginning of the interaction zone of contrarotating layers. It is established that the areas with the most unstable flow are localized in the flow vortex core. Three zones can be distinguished in the vortex core: a zone of weak instability with local Richardson numbers to Ri = –1, passing into a zone of flow destabilization with high negative values of Richardson numbers Ri = –10 to –100, in turn, transforming into a zone with rapidly increasing instability up to Ri = –1000. This is a zone of loss of flow stability, culminating in the “ortex breakdown”.

Hydrodynamic structure of laminar flows with oppositely-swirled coaxial layers

The article is devoted to the theoretical study of hydrodynamics of laminar flows with coaxial layers swirled in opposite directions and moving along the pipe. Such flows in a turbulent range have a wide practical application potential in technologies of dissipation of mechanical energy and mixing multiphase and heterogeneous media in microbiology, chemistry, ecology, heat engineering, power engineering, engine and rocket engineering. The article describes the tensor of viscous tangents (τii) and normal (σii) stresses. The questions of stability of flow according to the Rayleigh (Ra) and Richardson (Ri) criteria are considered. Calculation formulas and graphs of radial-axial distributions of viscous stress components, local stability zones are given, the point of “crisis and decay of the flow” or “vortex breakdown” is indicated. The solutions are obtained in the form of Fourier-Bessel series. The analysis of the hydrodynamic structure of the flow is made.

Investigation of Kelvin-Helmholtz instability in the stable boundary layer using large eddy simulation

We conducted a large eddy simulation of the stable boundary layer in order to investigate the coherent structure of the Kelvin–Helmholtz instability (KHI). The simulations were performed using the initial conditions based on the Beaufort Sea Arctic Stratus Experiment. We used the Richardson criteria and the linear stability analysis methods to detect the KHI and to adopt the eigenvalue and the two-point correlation methods to identify the vortex cores near the KHI region. In the two-point correlation analysis, the rotating configuration of the KHI varied in angles and lengths, according to the difference in the distance to the inversion layer. These vortex cores were divided into four components in different directions, defined by the signs of the x and y vorticities (Wx and Wy, respectively), and the vortex cores of the two components related to the negative Wy were elongated along the streamwise direction. The ratio between the sweeps and the ejections exhibited a linear trend as the boundary layer became more stable. Also, the sweep motion was dominant to the ejection motion for a high-stability index of 1.63. Furthermore, the plot of the vortex angles versus the stability index illustrated a linear relationship, indicating that the varying trends of the vortex angles were independent from the distance to the inversion layer in a sensitivity study of the vortex angle.

Stability of a Gaussian pancake vortex in a stratified fluid

AbstractVortices in stably stratified fluids generally have a pancake shape with a small vertical thickness compared with their horizontal size. In order to understand what mechanism determines their minimum thickness, the linear stability of an axisymmetric pancake vortex is investigated as a function of its aspect ratio $\alpha $, the horizontal Froude number ${F}_{h} $, the Reynolds number $\mathit{Re}$ and the Schmidt number $\mathit{Sc}$. The vertical vorticity profile of the base state is chosen to be Gaussian in both radial and vertical directions. The vortex is unstable when the aspect ratio is below a critical value, which scales with the Froude number: ${\alpha }_{c} \sim 1. 1{F}_{h} $ for sufficiently large Reynolds numbers. The most unstable perturbation has an azimuthal wavenumber either $m= 0$, $\vert m\vert = 1$ or $\vert m\vert = 2$ depending on the control parameters. We show that the threshold corresponds to the appearance of gravitationally unstable regions in the vortex core due to the thermal wind balance. The Richardson criterion for shear instability based on the vertical shear is never satisfied alone. The dominance of the gravitational instability over the shear instability is shown to hold for a general class of pancake vortices with angular velocity of the form $\tilde {\Omega } (r, z)= \Omega (r)f(z)$ provided that $r\partial \Omega / \partial r\lt 3\Omega $ everywhere. Finally, the growth rate and azimuthal wavenumber selection of the gravitational instability are accounted well by considering an unstably stratified viscous and diffusive layer in solid body rotation with a parabolic density gradient.

Indications of Stratified Turbulence in a Mechanistic GCM

Abstract The horizontal kinetic energy spectrum and its budget are analyzed on the basis of a general circulation model with simplistic parameterizations of radiative and latent heating. A spectral truncation at total wavenumber 330 is combined with a level spacing of either ~200 m or ~1.5 km from the midtroposphere to the lower stratosphere. The subgrid-scale parameterization consists of a Smagorinsky-type anisotropic diffusion scheme that is scaled by a Richardson criterion for dynamic instability and combined with a stress-tensor-based hyperdiffusion that acts only on the very smallest resolved scales. Simulations with both vertical resolutions show a transition from the synoptic −3 to the mesoscale slope in the upper-tropospheric kinetic energy spectrum. Analysis of the spectral budget indicates that the mesoscale slope can be interpreted as stratified turbulence, as has been proposed in recent works of Lindborg and others, only when a high vertical resolution is applied. In this case, the mesoscale kinetic energy around 300–150 hPa is dominated by the nonrotational flow, and the forward horizontal energy cascade is accompanied by an equally strong forward spectral flux due to adiabatic conversion. This adiabatic conversion mainly results from a vertical potential energy flux that originates in the midtroposphere, where the mesoscale adiabatic conversion is negative. For a conventionally coarse vertical resolution, however, the mesoscale slope in the troposphere is dominated by the rotational flow, and the spectral flux due to adiabatic conversion is not comparable to that associated with horizontal advection.

CIRCULATION AND DISSIPATION ON HOT JUPITERS

Many global circulation models predict supersonic zonal winds and large vertical shears in the atmospheres of short-period jovian exoplanets. Using linear analysis and nonlinear local simulations, we investigate hydrodynamic dissipation mechanisms to balance the thermal acceleration of these winds. The adiabatic Richardson criterion remains a good guide to linear stability, although thermal diffusion allows some modes to violate it at very long wavelengths and very low growth rates. Nonlinearly, wind speeds saturate at Mach numbers $\approx 2$ and Richardson numbers $\lesssim 1/4$ for a broad range of plausible diffusivities and forcing strengths. Turbulence and vertical mixing, though accompanied by weak shocks, dominate the dissipation, which appears to be the outcome of a recurrent Kelvin-Helmholtz instability. An explicit shear viscosity, as well as thermal diffusivity, is added to ZEUS to capture dissipation outside of shocks. The wind speed is not monotonic nor single valued for shear viscosities larger than about $10^{-3}$ of the sound speed times the pressure scale height. Coarsening the numerical resolution can also increase the speed. Hence global simulations that are incapable of representing vertical turbulence and shocks, either because of reduced physics or because of limited resolution, may overestimate wind speeds. We recommend that such simulations include artificial dissipation terms to control the Mach and Richardson numbers and to capture mechanical dissipation as heat.

VIOLATION OF RICHARDSON'S CRITERION VIA INTRODUCTION OF A MAGNETIC FIELD

Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient $V'$ can only destabilize a stably stratified medium with squared Brunt-Vaisala frequency $N^2$ if $V'^2/4>N^2$. We find this is no longer true when the medium is a magnetized plasma. We investigate the effect of stable stratification on magnetic field and velocity profiles unstable to magneto-shear instabilities, i.e., instabilities which require the presence of both magnetic field and shear flow. We show that a family of profiles originally studied by Tatsuno & Dorland (2006) remain unstable even when $V'^2/4<N^2$, violating the Richardson criterion. However, not all magnetic fields can result in a violation of the Richardson criterion. We consider a class of flows originally considered by Kent (1968), which are destabilized by a constant magnetic field, and show that they become stable when $V'^2/4<N^2$, as predicted by the Richardson criterion. This suggests that magnetic free energy is required to violate the Richardson criterion. This work implies that the Richardson criterion cannot be used when evaluating the ideal stability of a sheared, stably stratified, and magnetized plasma. We briefly discuss the implications for astrophysical systems.

Correlation of HER-2 Status with Estrogen, Progesterone Receptors and Histological Grading in 122 Invasive Breast Carcinomas

Background and objective: Many laboratory &amp; clinical studies have suggested that there are important inverse relationships between expression of HER-2 oncoprotein and hormonal receptors(ER,PR),the prognosis &amp; treatment are also greatly depend on hormonal receptor of neoplastic cells to define these relationships using standard immunohistochemistry for HER-2,ER and PR studies were performed in addition to routine histopahtological grading of carcinoma of the breast. Methods: Between January 2006 and December 2008 at histopathology lab of Rezgary hospital &amp; private lab, (122) women who were operated on for diagnostic excisional biopsies of the breast cancers to allow analysis of routinely resected tissue. Quantitative expression of HER-2,ER and PR was measured on the resected samples of the breast cancers with cutoff points HER-2,ER and PR positivity were 10.6%,5.5%,5% respectively in addition to routine study of histopathology for grading of cancers according to Nottingham modified Bloom &amp; Richardson criteria. Results: Immunohistochemical analysis for ER, PR, and HER-2 were performed. ER and PR expression were decreased significantly in HER-2 positive tumors compared with HER- 2 negative tumors (ER,15.57%,vs 41.8% vs. and PR, 13.11% vs. 37.70%;). Even among HER-2+ tumors, the rate of ER or PR expression in high-grade tumors was significantly decreased compared with intermediate grade tumors. HER-2 was positive in 73.3% of grade 2 and 66.6% of grade 3 ductal carcinomas and 6.89 in grade 1 ductal carcinomas. HER-2 expression essentially in grades 2 and 3 ductal carcinomas, very few cases in grade 1 and correlated inversely with ER or PR expression. Although ER or PR expression is decreased in HER-2+ tumors, a substantial proportion of them still express ER or PR. Conclusion: The results of this study are consistent with the indication of inverse relationships between HER-2 and ER,PR increased ER and PR levels in low grade neoplastic tissue ,the low grade neoplasms responding to hormonal therapy while high grade responding to hormonal therapy while high grage responding to herceptin.

Sensitivity of the Upper Mesosphere to the Lorenz Energy Cycle of the Troposphere

AbstractThe concept of a mechanistic general circulation model that explicitly simulates the gravity wave drag in the extratropical upper mesosphere in a self-consistent fashion is proposed. The methodology consists of 1) a standard spectral dynamical core with high resolution, 2) idealized formulations of radiative and latent heating, and 3) a hydrodynamically consistent turbulent diffusion scheme with the diffusion coefficients based on Smagorinsky’s generalized mixing-length formulation and scaled by the Richardson criterion. The model reproduces various mean and variable features of the wave-driven general circulation from the boundary layer to the mesopause region during January.The dissipation of mesoscale kinetic energy (defined as the frictional heating due to the mesoscale flow) in the extratropical troposphere is found to indicate the tropospheric gravity wave sources relevant for the mesosphere/lower thermosphere. This motivates a sensitivity experiment in which the large-scale differential heating is perturbed such that the Lorenz energy cycle as measured by the globally integrated frictional heating becomes stronger. As a result, both the resolved gravity wave activity and the dissipation of mesoscale kinetic energy in the extratropical troposphere are amplified. These changes have strong remote effects in the summer mesopause region, where the gravity wave drag, the residual meridional wind, and the frictional heating shift to lower altitudes. Furthermore, temperatures decrease below the summer mesopause and increase farther up, which is accompanied by an anomalous eastward wind component around the mesopause.

Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula

Gravitational instability of a vertically thin, dusty sheet near the midplane of a protoplanetary disk has long been proposed as a way of forming planetesimals. Before Roche densities can be achieved, however, the dust-rich layer, sandwiched from above and below by more slowly rotating dust-poor gas, threatens to overturn and mix by the Kelvin-Helmholtz instability (KHI). Whether such a threat is real has never been demonstrated: the Richardson criterion for the KHI is derived for two-dimensional Cartesian shear flow and does not account for rotational forces. Here we present three-dimensional numerical simulations of gas-dust mixtures in a shearing box, accounting for the full suite of disk-related forces: the Coriolis and centrifugal forces, and radial tidal gravity. Dust particles are assumed small enough to be perfectly entrained in gas; the two fluids share the same velocity field but obey separate continuity equations. We find that the Richardson number Ri does not alone determine stability. The critical value of Ri below which the dust layer overturns and mixes depends on the height-integrated metallicity Σd/Σg (surface density ratio of dust to gas). Nevertheless, for Σd/Σg between 1 and 5 times solar, the critical Ri maintains a nearly constant value of ~0.1. Keplerian radial shear stabilizes those modes that would otherwise disrupt the layer at large Ri. If the height-integrated metallicity is at least ~5 times greater than the solar value of 0.01, then midplane dust densities can approach Roche densities. Such a metal-rich environment might be expected to produce gas giant planets having similarly supersolar metallicities.

Hormone receptor expression in male breast cancers.

SummaryMale breast cancers are rare but have been found in higher proportions in Black Africans. Prognostic factors for breast cancers include tumour size, grade and stage, and hormone receptor status. The hormone receptor status is an invaluable guide in the use of adjuvant endocrine therapy, but none of the reports available in the literature from Africa showed any receptor work.This study was conducted to determine the grade, lymph node status and hormone receptor status of male breast cancers in Ghana.Nine archival cases of male breast cancers from the Pathology Department of Korle Bu Teaching Hospital were selected and studied on the basis of the presence of enough material for immunocytochemistry. Haematoxylin and Eosin (H & E) stained slides were reviewed and graded by Bloom and Richardson's criteria. Lymph node status was also assessed and sections were stained for oestrogen and progesterone receptors.Seven of the nine tumours were invasive ductal carcinomas and six of these were grade II, and one was grade III. Four cases had axillary lymph nodes removed at surgery and three were positive for metastases. Six (66%) of the cases were positive for oestrogen receptors with an H score ranging from 20 to 300. Using the criteria of McCarty et al, positivity for oestrogen receptor was reduced to 44%, which is lower than for Caucasians. We believe that this may be explained by the fact that in Ghana male breast cancers are seen a decade earlier. Only two cases were positive for progesterone receptor with an H score of 10 and 75. The two cases positive for progesterone receptors were also positive for oestrogen receptors.It is concluded that hormone receptor study is important in deciding on endocrine and adjuvant chemotherapy in male breast cancers and should be done routinely to help surgeons plan postoperative management of these patients. We recommend further research in this area.

Instabilities of spiral shocks – I. Onset of wiggle instability and its mechanism

We found that loosely wound spiral shocks in an isothermal gas disk caused by a non-axisymmetric potential are hydrodynamically unstable, if the shocks are strong enough. High resolution, global hydrodynamical simulations using three different numerical schemes, i.e. AUSM, CIP, and SPH, show similarly that trailing spiral shocks with the pitch angle of larger than � 10 ◦ wiggle, and clumps are developed in the shock-compressed layer. The numerical simulations also show clear wave crests that are associated with ripples of the spiral shocks. The spiral shocks tend to be more unstable in a rigidly rotating disk than in a flat rotation. This instability could be an origin of the secondary structures of spiral arms, i.e. the spurs/fins, observed in spiral galaxies. In spite of this local instability, the global spiral morphology of the gas is maintained over many rotational periods. The Kelvin-Helmholtz (K-H) instability in a shear layer behind the shock is a possible mechanism for the wiggle instability. The Richardson criterion for the K-H stability is expressed as a function of the Mach number, the pitch angle, and strength of the background spiral potential. The criterion suggests that spiral shocks with smaller pitch angles and smaller Mach numbers would be more stable, and this is consistent with the numerical results.

Significance of immunohistochemical c-ErbB-2 product localisation pattern for prognosis in human breast cancer.

Breast cancer is an increasingly important cause of illness and death among women. In recent years several novel prognostic determinants of breast cancer have been identified, including c-ErbB-2. In this study, expression of c-ErbB-2 in breast carcinoma was correlated with axillary lymph node metastases and disease outcome. The expression of c-ErbB-2 oncoprotein was analysed in 315 tumor specimens of infiltrating ductal carcinoma of breast. They were categorized according to the modified Bloom and Richardson criteria into three histological grades. These patients also had axillary lymph nodes sampling. The expression of c-ErbB-2 oncoprotein was analysed immunohistochemically. Over expression of c-ErbB-2 were observed in 39.36% tumors. Axillary lymph node metastasis had significant correlation with intensified positivity of c-ErbB-2. C-ErbB-2 positive patients did show resistance to chemotherapy when compared for recurrence and distant metastases following surgery (p< 0.05). At a median follow-up of 48 months in c-ErbB-2 positive patients, the overall survival was 3.0 years and disease free survival was 2.5 years. c-ErbB-2 negative tumor patients showed a far better survival. In this group the overall survival was 4.44 years and the disease free survival was 3.78 years. These findings reinforce the view that c-ErbB-2 immunohistochemical detection is of help in detecting a subgroup of breast carcinoma patients who are at high risk. This may also be of particular relevance in decisions regarding adjuvant chemotherapy to these patients.

Three-dimensional centrifugal-type instabilities of two-dimensional flows in rotating systems

This paper deals with the stability of incompressible inviscid planar basic flows in a rotating frame. We give a sufficient condition for such flows to undergo three-dimensional shortwave centrifugal-type instabilities. This criterion reduces to the Bradshaw–Richardson (1969) or Pedley (1969) criterion in the specific case of parallel shear flows subject to rotation, to Rayleigh’s centrifugal criterion (1916) in the case of axisymmetric vortices in inertial frames, to the Kloosterziel and van Heijst (1991) criterion in the case of axisymmetric vortices subject to rotation and to Bayly’s criterion (1988) in the case of general two-dimensional flows in inertial frames. The criterion states that a steady 2D basic flow subject to rotation Ω is unstable if there exists a streamline for which at each point 2(V/R+Ω)(W+2Ω)&amp;lt;0 where W is the vorticity of the streamline, ℛ is the local algebraic radius of curvature of the streamline and V is the local norm of the velocity. If this condition is satisfied then the flow is unstable according to the geometrical optics method introduced by Lifschitz and Hameiri (1991), which consists in following wave packets along the flow trajectories using a Wentzel–Kramers–Brillouin formalism. When the streamlines are closed, it is further shown that a localized unstable normal mode can be constructed in the vicinity of a streamline. As an application, this new criterion is used to study the centrifugal-type instabilities in the Stuart vortices, which is a family of exact solutions describing a row of periodic co-rotating eddies. For each solution of that family and for each rotation parameter f=2Ω, we give the unstable streamline interval, according to the criterion of instability. This criterion gives only a sufficient condition of centrifugal instability. The equations of the geometrical optics method are therefore numerically solved to obtain the true centrifugally unstable streamline intervals. It turns out that our criterion gives excellent results for highly concentrated vortices, i.e., the two approaches yield the same unstable streamline intervals. In less concentrated vortices, some streamlines undergo centrifugal instability although our criterion is not fulfilled. From these numerical results, another criterion of centrifugal instability for a flow with closed streamlines is conjectured which reduces to the change of sign of the absolute vorticity W+2Ω somewhere in the flow.

Stability Condition of the Kelvin-Helmholtz Instability for the Two-Component Protogalaxy

Within the context of the evolution of two-component protogalaxies, we discuss the stability condition of the Kelvin-Helmholtz (KH) instability on a boundary where evaporation of a denser component (cloud) or condensation of a diffuser component (hot gas) is expected. It has been stressed that the stability condition for the KH instability may determine the global properties of protogalaxies. However, discontinuous phase transition layer was assumed between the two phases in previous studies, though that layer is never a step condition. It is known that when a density continuity on the boundary is concerned, the KH instability is stabilized by gravity if the well-known Richardson criterion is satisfied : J &amp;gt; 0.25, where J is called the Richardson number. Especially, for the physical parameters of the two-component model of a protogalaxy, we find that J is much smaller than 0.25. The Richardson criterion is the stable condition due to gravity (we do not judge whether the adopted condition becomes unstable). Then, the smallness of J means that we can neglect the stabilization due to the self-gravity of the denser cloud component. Our conclusion supports the justification of the stability condition for the cloud phase given by the previous study.