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A stochastic minimization method for a real-space wavefunction, Ψ(r,r...r), constrained to a chosen density, ρ(r), is developed. It enables the explicit calculation of the Levy constrained search F[ρ]=min <Ψ|T+V|Ψ>, that gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[ρ] for densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives δF/δρ(r) and δF/δρ(r)δρ(r'). For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, E, without needing to solve the Schrödinger equation.
This article was published in the following journal.
Name: The journal of physical chemistry letters
Historical methods of functional development in density functional theory have often been guided by analytic conditions that constrain the exact functional one is trying to approximate. Recently, mach...
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The SCCOR Minorities study will recruit minority participants from the COPDGene cohort, in whom the University of Pittsburgh has already obtained baseline and five year data, in order to e...
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The Rapid Study: Randomized Phase II Study To Expedite Allogeneic Transplant With Immediate Haploidentical Plus Unrelated Cord Donor Search Versus Matched Unrelated Donor Search For AML And High-Risk MDS Patients
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Separation of particles according to density by employing a gradient of varying densities. At equilibrium each particle settles in the gradient at a point equal to its density. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)
The amount of mineral per square centimeter of BONE. This is the definition used in clinical practice. Actual bone density would be expressed in grams per milliliter. It is most frequently measured by X-RAY ABSORPTIOMETRY or TOMOGRAPHY, X RAY COMPUTED. Bone density is an important predictor for OSTEOPOROSIS.
Conditions with abnormally low levels of LIPOPROTEINS in the blood. This may involve any of the lipoprotein subclasses, including ALPHA-LIPOPROTEINS (high-density lipoproteins); BETA-LIPOPROTEINS (low-density lipoproteins); and PREBETA-LIPOPROTEINS (very-low-density lipoproteins).
A 6.6-kDa protein component of VERY-LOW-DENSITY LIPOPROTEINS; INTERMEDIATE-DENSITY LIPOPROTEINS; and HIGH-DENSITY LIPOPROTEINS. Apo C-I displaces APO E from lipoproteins, modulate their binding to receptors (RECEPTORS, LDL), and thereby decrease their clearance from plasma. Elevated Apo C-I levels are associated with HYPERLIPOPROTEINEMIA and ATHEROSCLEROSIS.
Cholesterol which is contained in or bound to very low density lipoproteins (VLDL). High circulating levels of VLDL cholesterol are found in HYPERLIPOPROTEINEMIA TYPE IIB. The cholesterol on the VLDL is eventually delivered by LOW-DENSITY LIPOPROTEINS to the tissues after the catabolism of VLDL to INTERMEDIATE-DENSITY LIPOPROTEINS, then to LDL.