3,673 research outputs found
Two Mappings Related To Semi-Inner Products And Their Applications in Geometry of Normed Linear Spaces
In this paper we introduce two mappings associated with the lower and upper semiinner product (.,.)i and (.,.)s and with semi-inner products [.,.] (in the sense of Lumer) which generate the norm of a real normed linear space, and study properties of monotonicity and boundedness
of these mappings. We give a refinement of the Schwarz inequality, applications to the Birkhoff orthogonality, to smoothness of normed linear spaces as well as to the characterization of best approximants
Some GrĂĽss' Type Inequalities in 2-Inner Product Spaces and Applications for Determinantal Integral Inequalities
Some new GrĂĽss type inequalities in 2-inner product spaces are given. Using this framework, some determinantal integral inequalities for synchronous functions are also derived
Any l-state solutions of the Woods-Saxon potential in arbitrary dimensions within the new improved quantization rule
The approximated energy eigenvalues and the corresponding eigenfunctions of
the spherical Woods-Saxon effective potential in dimensions are obtained
within the new improved quantization rule for all -states. The Pekeris
approximation is used to deal with the centrifugal term in the effective
Woods-Saxon potential. The inter-dimensional degeneracies for various orbital
quantum number and dimensional space are studied. The solutions for the
Hulth\'{e}n potential, the three-dimensional (D=3), the -wave () and
the cases are briefly discussed.Comment: 15 page
A perturbative treatment for the energy levels of neutral atoms
Energy levels of neutral atoms have been re-examined by applying an
alternative perturbative scheme in solving the Schrodinger equation for the
Yukawa potential model with a modified screening parameter. The predicted shell
binding energies are found to be quite accurate over the entire range of the
atomic number up to 84 and compare very well with those obtained within the
framework of hyper-virial-Pade scheme and the method of shifted large-N
expansion. It is observed that the new perturbative method may also be applied
to the other areas of atomic physics.Comment: 18 page
ASCORE: an up-to-date cardiovascular risk score for hypertensive patients reflecting contemporary clinical practice developed using the (ASCOT-BPLA) trial data.
A number of risk scores already exist to predict cardiovascular (CV) events. However, scores developed with data collected some time ago might not accurately predict the CV risk of contemporary hypertensive patients that benefit from more modern treatments and management. Using data from the randomised clinical trial Anglo-Scandinavian Cardiac Outcomes Trial-BPLA, with 15 955 hypertensive patients without previous CV disease receiving contemporary preventive CV management, we developed a new risk score predicting the 5-year risk of a first CV event (CV death, myocardial infarction or stroke). Cox proportional hazard models were used to develop a risk equation from baseline predictors. The final risk model (ASCORE) included age, sex, smoking, diabetes, previous blood pressure (BP) treatment, systolic BP, total cholesterol, high-density lipoprotein-cholesterol, fasting glucose and creatinine baseline variables. A simplified model (ASCORE-S) excluding laboratory variables was also derived. Both models showed very good internal validity. User-friendly integer score tables are reported for both models. Applying the latest Framingham risk score to our data significantly overpredicted the observed 5-year risk of the composite CV outcome. We conclude that risk scores derived using older databases (such as Framingham) may overestimate the CV risk of patients receiving current BP treatments; therefore, 'updated' risk scores are needed for current patients
q-Integral inequalities associated with some fractional q-integral operators
In recent years fractional q-integral inequalities have been investigated by many authors. Therefore, the fractional q-integral inequalities have become one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Here, we aim to establish some new fractional q-integral inequality by using fractional q-integral operators. Relevant connections of the results presented here with earlier ones are also pointed out
"Double-trace" Deformations, Boundary Conditions and Spacetime Singularities
Double-trace deformations of the AdS/CFT duality result in a new perturbation
expansion for string theory, based on a non-local worldsheet. We discuss some
aspects of the deformation in the low energy gravity approximation, where it
appears as a change in the boundary condition of fields. We relate unique
features of the boundary of AdS to the worldsheet becoming non-local, and
conjecture that non-local worldsheet actions may be generic in other classes of
backgrounds.Comment: 21 pages, 2 figures, harvmac. v2: minor changes, references added,
version sent to JHEP. v3 minor correction
Non-commutative holography and scattering amplitudes in a large magnetic background
We study planar gluon scattering amplitudes and Wilson loops in
non-commutative gauge theory. Our main results are:
1. We find the map between observables in non-commutative gauge theory and
their holographic dual. In that map, the region near the boundary of the
gravitational dual describes the physics in terms of T-dual variables.
2. We show that in the presence of a large magnetic background and a UV
regulator, a planar gluon scattering amplitude reduces to a complex polygon
Wilson loop expectation value, dressed by a tractable polarization dependent
factor.Comment: 26 pages. v2: corrected section 4, reference adde
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