Alternatives for Measuring Hazardous Waste Reduction

PTI Project number 233U-4913FRHWRIC Project Number 89006

A Comparison of Three Sit-up Exercises for Improving Abdominal Strength and Endurance

Yessis claims that a sit-up which will bring greater muscle development to the entire abdominal wall ls the bench sit-up. In this sit-up, the abdominal muscles are responsible for flexion of the lower spine and involves the movement of the upper body toward the lower body. To perform the bench sit-up, the person sits crosswise on a bench with the pelvic girdle well supported and the feet on the floor. With the feet supported and the arms across the chest, the individual slowly leans backward until the trunk is slightly below horizontal, creating a slight hyperextension of the spine. The trunk is then raised upward to the original position by executing spinal flexion. The head is kept tilted slightly upward during the entire exercise. This exercise is geared more towards advanced exercisers due to the great involvement of abdominal and hip flexor muscles. Additionally, there are numerous exercise devices that are marketed commercially which claim to do wonders for the abdominal region however the validity of these devices is questionable. Most, if not all, are marketed without substantial research to support their claims. It is in the best interest of the public to determine if these, as well as more conventional ways of doing abdominal exercises are effective in increasing abdominal strength and abdominal endurance. The purpose of this study was to compare three methods of improving abdominal strength and endurance. More specifically, the study sought to determine whether three distinctly different sit-up exercises, the Rowing Exerciser, the Sit-N-Trim exercise, and the crunch exercise, were similar or different in their ability to effect changes in muscular strength and/or muscular endurance. The fundamental question to be answered by this study is, is there a sit-up exercise that will improve strength and endurance more than any other? The specific hypotheses tested were as follows: 1. There will be no significant difference in strength gain between subjects in the Sit-N-Trim and crunch groups but there will be a significant difference between these two groups and the Rowing Exerciser group. 2. There will be no significant difference in endurance gain between subjects in the Sit-N-Trim and the crunch groups but there will be a difference between these two groups and the Rowing Exerciser group

Fr\'echet frames, general definition and expansions

We define an {\it $(X_1,\Theta, X_2)$-frame} with Banach spaces $X_2\subseteq X_1$, $|\cdot|_1 \leq |\cdot|_2$, and a $BK$-space (\Theta, \snorm[\cdot]). Then by the use of decreasing sequences of Banach spaces ${X_s}_{s=0}^\infty$ and of sequence spaces ${\Theta_s}_{s=0}^\infty$, we define a general Fr\' echet frame on the Fr\' echet space $X_F=\bigcap_{s=0}^\infty X_s$. We give frame expansions of elements of $X_F$ and its dual $X_F^*$, as well of some of the generating spaces of $X_F$ with convergence in appropriate norms. Moreover, we give necessary and sufficient conditions for a general pre-Fr\' echet frame to be a general Fr\' echet frame, as well as for the complementedness of the range of the analysis operator $U:X_F\to\Theta_F$.Comment: A new section is added and a minor revision is don

A note on a canonical dynamical r-matrix

It is well known that a classical dynamical $r$-matrix can be associated with every finite-dimensional self-dual Lie algebra \G by the definition $R(\omega):= f(\mathrm{ad} \omega)$, where \omega\in \G and $f$ is the holomorphic function given by $f(z)={1/2}\coth \frac{z}{2}-\frac{1}{z}$ for z\in \C\setminus 2\pi i \Z^*. We present a new, direct proof of the statement that this canonical $r$-matrix satisfies the modified classical dynamical Yang-Baxter equation on \G.Comment: 17 pages, LaTeX2

Teaching schools evaluation. Research Brief

This Research Brief reports the findings from a two-year study (2013-15) in to the work of teaching schools and their alliances commissioned by the National College for Teaching and Leadership (NCTL). The broad aim of the study was to investigate the effectiveness and impact of teaching schools on improvement, and identify the quality and scope of external support that are required to enhance these . This was achieved through combining qualitative and quantitative data collection and analysis derived from three research activities: case studies of 26 teaching schools alliances (TSAs), a national survey of the first three cohorts of 345 TSAs, and secondary research and analysis of national performance and inspection results

Bohl-Perron type stability theorems for linear difference equations with infinite delay

Relation between two properties of linear difference equations with infinite delay is investigated: (i) exponential stability, (ii) \l^p-input \l^q-state stability (sometimes is called Perron's property). The latter means that solutions of the non-homogeneous equation with zero initial data belong to \l^q when non-homogeneous terms are in \l^p. It is assumed that at each moment the prehistory (the sequence of preceding states) belongs to some weighted \l^r-space with an exponentially fading weight (the phase space). Our main result states that (i) $\Leftrightarrow$ (ii) whenever $(p,q) \neq (1,\infty)$ and a certain boundedness condition on coefficients is fulfilled. This condition is sharp and ensures that, to some extent, exponential and \l^p-input \l^q-state stabilities does not depend on the choice of a phase space and parameters $p$ and $q$, respectively. \l^1-input \l^\infty-state stability corresponds to uniform stability. We provide some evidence that similar criteria should not be expected for non-fading memory spaces.Comment: To be published in Journal of Difference Equations and Application

Psychometric evaluation of the Pain Assessment in Advanced Dementia scale in an acute general hospital setting

BACKGROUND: People with dementia are at risk of unplanned hospital admissions and commonly have painful conditions. Identifying pain is challenging and may lead to undertreatment. The psychometric properties of the Pain Assessment in Advanced Dementia (PAINAD) scale, in medical inpatients with dementia have not been evaluated. METHODS: A secondary data analysis from a longitudinal study of 230 people with dementia admitted to two acute general hospitals in London, UK. Internal consistency, inter-rater reliability, test-retest reliability, concurrent validity, construct validity and discriminant validity of PAINAD were tested at rest and in movement. RESULTS: This predominantly female (65.7%) sample had a mean age of 87.2 (Standard Deviation; SD = 5.92) years. Inter-rater reliability showed an intra-class correlation (ICC) of 0.92 at rest and 0.98 in movement, test-retest reliability ICC was 0.54 at rest and 0.66 in movement. Internal consistency was 0.76 at rest and 0.80 in movement (Cronbach's α). Concurrent validity was weak between PAINAD and a self-rating level of pain (Kendall's Tau; τ = 0.29; p > 0.001). There was no correlation between PAINAD and a measure of behavioural and psychological symptoms of dementia, suggesting no evidence of convergent validity. PAINAD scores were higher during movement than rest, providing evidence of discriminant validity (z = -8.01, p < 0.001). CONCLUSIONS: We found good inter-rater reliability and internal consistency. The test-retest reliability was modest. This study raises concerns about the validity of the PAINAD in general acute hospitals. This provides an insight into pain assessment in general acute hospitals which may inform further refinements of the PAINAD

Higher order Schrodinger and Hartree-Fock equations

The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb potentials is developed. Finally, the existence of associated ground states for the odd-order equations is proved. This renders these quantum equations relevant for physics.Comment: 19 pages, to appear in J. Math. Phy

Self-Adjointness of Generalized MIC-Kepler System

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for \tilde l=0, the system admits a 1-parameter family of self-adjoint extensions and for \tilde l \neq 0 but \tilde l <{1/2}, it has also a 1-parameter family of self-adjoint extensions.Comment: 11 pages, Latex, no figur