i=1 H(ri); (5) HΨ(r1, r2, · · · ) = EΨ(r1, r2, · · · ). (6) (Note: For simplicity, unless necessary, we often write r as r.) Since there is no interaction between particles, the Schrodinger equation is separable. Assume Ψ(r1, r2, · · · , rN ) = φ(r1)φ(r2) · · ·φ(rN ), (7) then Hφαi(ri) = εαiφαi(ri), i = 1, 2, · · ·N. (8) Manybody eigenstate is a product of 1-particle states, Ψα1,α2,···(r1, r2, ...

A fl uorescence sensor array is being developed to detect explosives at ambient temperature and atmospheric conditions. The sensor platform uses a multilayer substrate that serves to amplify the emission signal by more than three orders of magnitude, improving the sensor response accordingly. Studies to understand the mechanism of the signal amplifi cation are being undertaken so that the senso...

Given a function f 2 L 2 (Q), Q := 0; 1) 2 and a real number t > 0, let U (f; t) := inf g2BV(Q) kf ? gk 2 L 2 (I) + t V Q (g); where the innmum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for ...

We present exact results for the dynamical structure function, i.e. the densitydensity correlations for the 1/r2 system of interacting particles at three special values of the coupling constant. The results are interpreted in terms of exact excitations of the model which are available from Bethe’s Ansatz, thereby throwing light on the quasi-particle content of the elementary excitations. We als...

For simplicity, we adopt the following convention: x, x0, y, y0, r are real numbers, z, z0 are elements of R2, Z is a subset of R2, f , f1, f2 are partial functions from R2 to R, R is a rest, and L is a linear function. Next we state two propositions: (1) domproj(1, 2) = R2 and rng proj(1, 2) = R and for all elements x, y of R holds (proj(1, 2))(〈x, y〉) = x. (2) domproj(2, 2) = R2 and rng proj(...

(1) Let X be a real linear space and R1, R2 be finite sequences of elements of X. If lenR1 = lenR2, then ∑ (R1 +R2) = ∑ R1 + ∑ R2. (2) Let X be a real linear space and R1, R2, R3 be finite sequences of elements of X. If lenR1 = lenR2 and R3 = R1−R2, then ∑ R3 = ∑ R1− ∑ R2. (3) Let X be a real linear space, R1, R2 be finite sequences of elements of X, and a be an element of R. If R2 = aR1, then ...

Let M be a compact, orientable, irreducible, ∂-irreducible, anannular 3manifold with one component T of ∂M a torus. A slope r on T is a T isotopy class of essential, unoriented, simple closed curves on T , and the distance between two slopes r1 and r2, denoted by 4(r1, r2), is the minimal geometric intersection number among all the curves representing the slopes. For a slope r on T , we denote ...

The self-assembly in solution and adsorption at the air-water interface, measured by small-angle neutron scattering, SANS, and neutron reflectivity, NR, of the monorhamnose and dirhamnose rhamnolipids (R1, R2) and their mixtures, are discussed. The production of the deuterium-labeled rhamnolipids (required for the NR studies) from a Pseudomonas aeruginosa culture and their separation into the p...