A Generalisation of an Ostrowski Inequality in Inner Product Spaces

A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given

An Inequality in Metric Spaces

In this note we establish a general inequality valid in metric spaces that is related to the polygonal inequality and admits also a natural geometrical interpretation. Particular instances of interest holding in normed linear spaces and inner product spaces are pointed out as well

Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass

The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.Comment: 13 page

Exact Spin and Pseudo-Spin Symmetric Solutions of the Dirac-Kratzer Problem with a tensor potential via Laplace Transform Approach

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectra is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agrement with the ones given in literature. The numerical results are also given in a table for different parameter values.Comment: 8 page

Following severe injury, hypocholesterolemia improves with convalescence but persists with organ failure or onset of infection

INTRODUCTION: Our primary objective was to determine the impact of traumatic injury, onset of infection, organ/metabolic dysfunction, and mortality on serum cholesterol. METHODS: During 676 surgical intensive care unit (SICU) days, 28 ventilated trauma patients underwent daily measurement of white blood cell (WBC) count and differential, cholesterol, arterial oxygen tension/fractional inspired oxygen, bilirubin, glucose, creatinine, and bicarbonate. With the onset of infection, WBC response was considered positive if the WBC count was 16.0 or greater, immature neutrophils were 10% or greater, or WBC count increased by 20%. Cholesterol response was considered positive if cholesterol decreased or failed to increase by 10%. RESULTS: Injury Severity Score was 30.6 ± 8.6 and there were 48 infections. Initial cholesterol was decreased (119 ± 44 mg/dl) compared with expected values from a database (201 ± 17 mg/dl; P < 0.0001). The 25 survivors had higher cholesterol at SICU discharge (143 ± 35 mg/dl) relative to admission (112 ± 37 mg/dl; P < 0.0001). In the three patients who died, the admission cholesterol was 175 ± 62 mg/dl and the cholesterol at death was 117 ± 27 mg/dl. The change in percentage of expected cholesterol (observed value divided by expected value) from admission to discharge was different for patients surviving (16 ± 19%) and dying (-29 ± 19%; P = 0.0005). With onset of infection, the WBC response was positive in 61% and cholesterol response was positive in 91% (P = 0.001). Percentage of expected cholesterol was decreased with each system dysfunction: arterial oxygen tension/fractional inspired oxygen < 350, creatinine > 2.0 mg/dl, glucose > 120 mg/dl, bilirubin > 2.5 mg/dl, and bicarbonate ≥ 28 or ≤ 23 (P < 0.01). Percentage of expected cholesterol decreased as the number of dysfunctions increased (P = 0.0001). CONCLUSION: Hypocholesterolemia is seen following severe injury. Convalescing patients (ready for SICU discharge) have improved cholesterol levels, whereas dying patients appear to have progressive hypocholesterolemia. Decreasing or fixed cholesterol levels suggest the development of infection or organ/metabolic dysfunction. Cholesterol responses are more sensitive for the onset of infection than are WBC responses. Sequential cholesterol monitoring is recommended for patients with severe trauma