Lie and Riccati Linearization of a Class of Liénard Type Equations

We construct a linearizing Riccati transformation by using an ansatz and a linearizing point transformation utilizing the Lie point symmetry generators for a three-parameter class of Liénard type nonlinear second-order ordinary differential equations. Since the class of equations also admits an eight-parameter Lie group of point transformations, we utilize the Lie-Tresse linearization theorem to obtain linearizing point transformations as well. The linearizing transformations are used to transform the underlying class of equations to linear third- and second-order ordinary differential equations, respectively. The general solution of this class of equations can then easily be obtained by integrating the linearized equations resulting from both of the linearization approaches. A comparison of the results deduced in this paper is made with the ones obtained by utilizing an approach of mapping the class of equations by a complex point transformation into the free particle equation. Moreover, we utilize the linearizing Riccati transformation to extend the underlying class of equations, and the Lie-Tresse linearization theorem is also used to verify the conditions of linearizability of this new class of equations

Simulator-based learning, the Dunning-Kruger effect and the newly-‘qualified’ Officer of the Watch.

Does simulator-based learning promote inappropriate confidence in the mind of a newly qualified Officer of the Watch

Utilizing Functional Genomics Screening to Identify Potentially Novel Drug Targets in Cancer Cell Spheroid Cultures

The identification of functional driver events in cancer is central to furthering our understanding of cancer biology and indispensable for the discovery of the next generation of novel drug targets. It is becoming apparent that more complex models of cancer are required to fully appreciate the contributing factors that drive tumorigenesis in vivo and increase the efficacy of novel therapies that make the transition from preclinical models to clinical trials. Here we present a methodology for generating uniform and reproducible tumor spheroids that can be subjected to siRNA functional screening. These spheroids display many characteristics that are found in solid tumors that are not present in traditional two-dimension culture. We show that several commonly used breast cancer cell lines are amenable to this protocol. Furthermore, we provide proof-of-principle data utilizing the breast cancer cell line BT474, confirming their dependency on amplification of the epidermal growth factor receptor HER2 and mutation of phosphatidylinositol-4,5-biphosphate 3-kinase (PIK3CA) when grown as tumor spheroids. Finally, we are able to further investigate and confirm the spatial impact of these dependencies using immunohistochemistry.Open Access fees were supported by Nexcelom Bioscience, LLCThis work was funded by Breast Cancer Now. RN is the recipient of a Breast Cancer Now Career Development Fellowship (2011MaySF01

Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest

IMPULSIVE DIFFERENTIAL SYSTEM WITH VARIABLE TIMES

Results on mild solution of nonclassical ordinary differential equations(NODE) with variable times and impulsive conditions are studied. The moments of impulsive effect depend on the solution

Ethnic disparity in access to the memory assessment service between South Asian and white British older adults in the United Kingdom: A cohort study

Background: Equality of access to memory assessment services by older adults from ethnic minorities is both an ethical imperative and a public health priority.Objective: To investigate whether timeliness of access to memory assessment service differs between older people of White British and South Asian ethnicity.Design: Longitudinal cohort.Setting: Nottingham Memory Study; outpatient secondary mental healthcare.Subjects: Our cohort comprised 3,654 White British and 32 South Asian older outpatients.Methods: The criterion for timely access to memory assessment service was set at 90 days from referral. Relationships between ethnicity and likelihood of timely access to memory assessment service were analysed using binary logistic regression. Analyses were adjusted for socio-demographic factors, deprivation and previous access to rapid response mental health services.Results: Among White British outpatients, 2,272 people (62.2%) achieved timely access to memory assessment service. Among South Asian outpatients, fourteen people (43.8%) achieved timely access to memory assessment service. After full adjustment, South Asian outpatients had a 0.47-fold reduced likelihood of timely access, compared to White British outpatients (odds ratio 0.47, 95% confidence interval 0.23-0.95, p-value=0.035). The difference became non-significant when restricting analyses to outpatients reporting British nationality or English as first language. Older age, lower index of deprivation and previous access to rapid response mental health services were associated with reduced likelihood of timely access, while gender was not.Conclusions: In a UK mental healthcare service, older South Asian outpatients are less likely to access dementia diagnostic services in a timely way, compared to White British outpatients

Association between mid-wall late gadolinium enhancement and sudden cardiac death in patients with dilated cardiomyopathy and mild and moderate left ventricular systolic dysfunction

Background—Current guidelines only recommend the use of an implantable cardioverter defibrillator (ICD) in patients with dilated cardiomyopathy (DCM) for the primary prevention of sudden cardiac death (SCD) in those with a left ventricular ejection fraction (LVEF)35%. Patients with a LVEF>35% also have low competing risks of death from non-sudden causes. Therefore, those at high-risk of SCD may gain longevity from successful ICD therapy. We investigated whether late gadolinium enhancement cardiovascular magnetic resonance (LGE-CMR) identified patients with DCM without severe LV systolic dysfunction at high-risk of SCD. Methods—We prospectively investigated the association between mid-wall late gadolinium enhancement (LGE) and the pre-specified primary composite outcome of SCD or aborted SCD amongst consecutive referrals with DCM and a LVEF≥40% to our center between January 2000 and December 2011, who did not have a pre-existing indication for ICD implantation. Results—Of 399 patients (145 women, median age 50 years, median LVEF 50%, 25.3% with LGE) followed for a median of 4.6 years, 18 of 101 (17.8%) patients with LGE reached the pre-specified end-point, compared to 7 of 298 (2.3%) without (HR 9.2; 95% CI 3.9-21.8; p5% compared to those without LGE were 10.6 (95%CI 3.9-29.4), 4.9 (95% CI 1.3-18.9) and 11.8 (95% CI 4.3-32.3) respectively. Conclusions—Mid-wall LGE identifies a group of patients with DCM and LVEF≥40% at increased risk of SCD and low-risk of non-sudden death who may benefit from ICD implantation

EFFECT OF FEEDING FREQUENCY ON THE GROWTH PERFORMANCE OF BEETAL GOAT KIDS DURING WINTER SEASON

ABSTRACT Eighteen Beetal goat kids of about same age (one month) and average weight (3.2 kg) were selected from the prevailing flock and were divided randomly into three groups with 6 replicates in each group. These kids were kept separately to study the effect of feeding frequency on the growth performance during winter season. Green fodder was offered adlibitum and concentrate was given @ 1% of the body weight to each kid. Group A (control), B and C were fed two, three and four times daily, respectively. The parameters studied were feed intake, weight gain, body measurements like height, girth and length, environmental temperature and relative humidity. There was a significant difference in the DMI (P<0.01), weight gain (P<0.05), body height (P<0.01) between treatments (feeding frequency). Body girth and body length also had a significant difference (P<0.05) for group A with B and C where as non significant results were found between kids of group B and C on fortnightly basis. The kids of group C performed well in terms of weekly body weight gain, daily dry matter intake, and body measurement as compared to group A and B