Touching points of s star-shaped set with an affine subspace

AbstractThe paper studies the following problem. Given a linear subspace L ⊂ Rn of dimension k, 1 ⩽ k ⩽ n – 1, the point x ∃ Rn, x ∉ L, and a star-shaped set A ⊂ Rn, characterize those τ> 0 for which L + x touches τA, and, if this is the case, describe the set τ cl(A)∩(L + x). Here A is star-shaped if λA ⊆ A for all 0 ⩽ λ ⩽ 1, L + x touches τA if L + x meets τA only on the boundary, and cl(A) means the closure of A. The problem is solved for two kinds of sets: convex A such that the origin θ is contained in the relative interior of A, and A equals to the closed unit ɭp-ball Gp for some 0 < p < 1. For convex A the set L⊥ ∩ A∗ plays a crucial role, where A∗ ≔ {z ∃ Rn:⇄z,y↩ ⩽ 1 for all y ∈ A} is the polar of A, and L⊊ is the orthogonal complement subspace to L. For Gp the problem is solved by a special geometrical construction based on “coordinate” subspaces RT such that L ∩ RT = {θ}

The Psychobiological Correlates Of Panic Attacks During In Vivo Exposure

This study examined in detail the psychobiological correlates of panic attacks experienced in panic disorder with agoraphobia. The cognitions, affect, and physiology of the six patients were monitored during in vivo exposure to their phobic situations. The results from these case studies showed that catastrophic cognitions are the key component of panic attacks. However, there was no clear-cut evidence to support an interaction among cognitions, affect, and physiology, which has been postulated by cognitive theories to be the central component of panic attacks and panic disorder with agoraphobia

Effectiveness of a self-help cognitive behavioural treatment program for problem gamblers: a randomised controlled trial

The study aimed to strengthen the scarce literature on self-help treatments for Problem Gambling (PG) by comparing the effectiveness of a Self-Help Cognitive Behavioral Treatment (SHCBT) program (n\ua0=\ua023) with a 6-week Waitlist condition (n\ua0=\ua032) in problem gamblers. Participants were community volunteers with gambling problems and were randomly allocated to the Waitlist and treatment conditions. Results showed significant improvements at post-treatment in gambling behaviors including frequency of gambling, average amount gambled per day and PG symptoms as well as a number of gambling correlates including psychological states (e.g., depression, anxiety and stress), gambling cognitions, gambling urges, gambling related self-efficacy, satisfaction with life, and quality of life among those who completed the SHCBT program, when compared with the waitlist condition. The effect size (partial η) ranged from .25 to .57 for all assessed outcomes that showed significant improvement from pre- to post-treatment. It was concluded that a self-help CBT program can be beneficial for treating community problem gamblers

Pelarutan Besi Selektif pada Korosi Baja Karbon dalam Larutan Buffer Asetat, Natrium Bikarbonat - CO2 Jenuh

 This work has investigate conditions which allow pitting corrosion of carbon steel in acetate buffered test solutions of pH 3.82, 4.12, 5.12 and 6.12, 0.2 M NaOAc and standard brine solutions, all of which contains 100 mg/L sodium bicarbonate and saturated with CO2. Corrosion rates is determined by corrosion wheel and corrosion bubble tests, while surface morphology is observed by electron microscopy (SEM) and metallographic optical microscopy, whereas surface deterioration as well as corroded lattice structure of the steel is monitored through measurements by X-ray Diffraction (XRD) patterns. The X-ray Diffraction Patterns of corroded carbon steel in any of the above test solutions exhibit a decrease in relative intensity of 110 and 200 lattice planes and an increase in the 211 lattice plane. The extent of decrease of the diffracted X-ray intensities increases with the increase in the percentage of corroded carbon steel coupon weight loss. This might reflect a selective dissolution of iron atoms situated in both lattice planes. It is suspected that this observation is due to the fact that 211 lattice plane has the smallest percentage of atomic occupancy among the three, thus it might have the greatest chance to be inserted with carbon atoms which in turn gives a protective effect toward iron atoms against further dissolution. Although, the corrosion process starts from the surface phase, this experiment reveals that X-ray diffraction pattern of the three lattice planes could be employed as some sort of carbon steel corrosion indicator. Consequently, corrosion inhibitor performance could be deduced from its ability to maintain diffraction pattern of the initial carbon steel specimen

A novel fluorescent probe for NAD-consuming enzymes

A novel, fluorescent NAD derivative is processed as substrate by three different NAD-consuming enzymes. The new probe has been used to monitor enzymatic activity in a continuous format by changes in fluorescence and, in one case, to directly visualize alternative reaction pathways

Reply: Familial ovarian screening: how to address abnormal TVU findings and its influence on the efficacy of screening?

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Biological modelling of the radiation dose escalation effect of regional hyperthermia in cervical cancer

Background Locoregional hyperthermia combined with radiotherapy significantly improves locoregional control and overall survival for cervical tumors compared to radiotherapy alone. In this study biological modelling is applied to quantify the effect of radiosensitization for three cervical cancer patients to evaluate the improvement in equivalent dose for the combination treatment with radiotherapy and hyperthermia. Methods The Linear-Quadratic (LQ) model extended with temperature-dependent LQ-parameters α and β was used to model radiosensitization by hyperthermia and to calculate the conventional radiation dose that is equivalent in biological effect to the combined radiotherapy and hyperthermia treatment. External beam radiotherapy planning was performed based on a prescription dose of 46Gy in 23 fractions of 2Gy. Hyperthermia treatment using the AMC-4 system was simulated based on the actual optimized system settings used during treatment. Results The simulated hyperthermia treatments for the 3 patients yielded a T50 of 40.1 °C, 40.5 °C, 41.1 °C and a T90 of 39.2 °C, 39.7 °C, 40.4 °C, respectively. The combined radiotherapy and hyperthermia treatment resulted in a D95 of 52.5Gy, 55.5Gy, 56.9Gy in the GTV, a dose escalation of 7.3–11.9Gy compared to radiotherapy alone (D95 = 45.0–45.5Gy). Conclusions This study applied biological modelling to evaluate radiosensitization by hyperthermia as a radiation-dose escalation for cervical cancer patients. This model is very useful to compare the effectiveness of different treatment schedules for combined radiotherapy and hyperthermia treatments and to guide the design of clinical studies on dose escalation using hyperthermia in a multi-modality setting