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In this paper, we consider a condition on subspaces in order to improve bounds given in the Bernstein's Lethargy Theorem (BLT) for Banach spaces. Let $d_1 \geq d_2 \geq \dots d_n \geq \dots > 0$ be an infinite sequence of numbers converging to $0$, and let $Y_1 \subset Y_2 \subset \dots\subset Y_n \subset \dots \subset X$ be a sequence of closed nested subspaces in a Banach space $X$ with the property that $\overline{Y}_{n}\subset Y_{n+1}$ for all $n\ge1$. We prove that for any $c \in (0,1]$, there exists an element $x_c \in X$ such that $$ c d_n \leq \rho(x_c, Y_n) \leq \min (4, \tilde{a}) c\, d_n. $$ Here, $\rho(x, Y_n)= \inf \{ ||x-y||: \,\,y\in Y_n\}$, $$\tilde{a} =\sup_{i\ge1}\sup_{\left \{ q_{i} \right \}}\left \{ a_{n_{i+1}-1}^{-3}\right \}$$ where the sequence $\{a_n\}$ is defined as: for all $ n \geq 1 $, $$ a_n = \inf_{l \geq n} \, \inf_{q \in \langle q_l, q_{l+1},\dots \rangle} \frac{\rho(q,Y_l)}{||q||} $$ in which each point $q_n$ is taken from $Y_{n+1} \setminus Y_{n}$, and satisfies $\inf\limits_{n\ge1} a_n > 0$. The sequence $\{n_i\}_{i\ge1}$ is given by %Theorem \ref{100}, $\{n_i\}$ satisfying (\ref{ni}) and $n_{i}\leq n

We provide a new representation of an $\mathbb R$-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the $\mathbb R$-trees with radial and river metrics, and these sets of metric rays. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by $\mathbb R$-trees., Comment: 17 pages, 805C05, 05C62, 60J65, 54E35 figures

The purpose of this study was to examine the multivariate relationship of the Test of English as a Foreign Language (TOEFL) and the First Certificate of English (FCE), administered by the University of Cambridge Local Examinations Syndicate, and to determine whether students' total score on the TOEFL or their overall score on the FCE tends to be a better predictor of their success at the University of Bahrain as measured by overall grade point average (GPA). Subjects were 86 students enrolled at the University of Bahrain. The multivariate prediction of GPA from the scores on the FCE was very accurate. Regression analyses revealed that the FCE Cloze and Sentence Transformation subscores were the only test scores that contributed to the prediction of the student's GPA and his or her GPA in English courses. The TOEFL section scores did not contribute enough to be maintained in the linear prediction model. Results indicate that the FCE is a better test instrument than the TOEFL, especially when English is being taught as a foreign language. Since the TOEFL test did not appear to be an effective predictor of students' academic achievement at the university level, using it as a test instrument in any of the major language courses taught at the university within an English as a Second Language context should be reconsidered. (Contains 7 tables and 22 references.) (Author/SLD)

Evaluates a short-term residential program utilizing a behavior modification program in an outpatient unit for adolescents with mostly conduct problems. Evaluation indicated predictors of outcome, including: age, gender, diagnosis, length of stay, father's presence, other treatments received, and presence of learning problems. Factors such as father's presence and absence of learning problems were associated with better outcome. Discusses other findings. (KW)

Reports a study undertaken in Bahrain secondary schools to assess the contribution of tape recorders to learning outcomes in English as a Second Language (ESL). Findings revealed that students' proficiency correlated significantly with their perception of the frequency and skill with which their teacher use a tape recorder. (20 references) (Author/CK)

Retrospectively examined adolescents from two time periods, diagnosed with adjustment disorder (n=72), for type of life stressors that initiated referrals to child psychiatry unit and compared them to control group of 42 referred adolescents with no psychopathology. Disappointment in relationships with family member or friend of opposite sex was main stressor. (Author/NB)