We prove in this note that the global geometric theta lifting for the pair (H,G) is compatible with the Whittaker normalization, where (H,G) = (SO2n, Sp2n), (Sp2n, SO2n+2), or (GLn, GLn+1). More precisely, let k be an algebraically closed field of characteristic p > 2. Let X be a smooth projective connected curve over k. For a stack S write D(S) for the derived category of étale constructible Q̄...

Mitogen-activated protein kinases (MAPKs), important in a large array of signalling pathways, are tightly controlled by a cascade of protein kinases and by MAPK phosphatases (MKPs). MAPK signalling efficiency and specificity is modulated by protein-protein interactions between individual MAPKs and the docking motifs in cognate binding partners. Two types of docking interactions have been identi...

We perform separation of direct and global components of light transport using the method introduced by Nayar et al. [2]. We illuminate the scene using multiple high frequency patterns and the direct and global components of illumination are obtained from the acquired images using the Nayar method, which is a closed-form, per-pixel solution. We use the DLP Lightcommander projector in near-infra...

By recurring to Geometric Probability methods it is shown that the coupling constants, αEM , αW , αC , associated with the electromagnetic, weak and strong (color) force are given by the ratios of measures of the sphere S and the Shilov boundaries Q3 =S 2 ×RP , squashed S, respectively, with respect to the Wyler measure ΩWyler[Q4] of the Shilov boundary Q4 =S ×RP 1 of the poly-disc D4 (8 real d...

Symmetry breaking of solitons in a class of one-dimensional parity-time (PT) symmetric complex potentials with cubic nonlinearity is reported. In generic PT-symmetric potentials, such symmetry breaking is forbidden. However, in a special class of PT-symmetric potentials V(x)=g(2)(x)+αg(x)+ig'(x), where g(x) is a real and even function and α a real constant, symmetry breaking of solitons can occ...

The object of the study is production and technological processes international road transport (PTP IRT) according to innovative approach conceptual idea technical energy saving in motor transport. Predictive assumptions about development – realization possibilities operational-simulation technical-evolutionary method complex analysis efficiency trains practice In course research production-tec...

Finally the Lagranage dual function is given by g(~λ, ~ν) = inf~x L(~x,~λ, ~ν) We now make a couple of simple observations. Observation. When L(·, ~λ, ~ν) is unbounded from below then the dual takes the value −∞. Observation. g(~λ, ~ν) is concave1 as it is the infimum of a set of affine2 functions. If x is feasible solution of program (10.2)(10.4), then we have the following L(x,~λ, ~ν) = f0(x)...

C be the normalization of Γ . Let g = (d− 1)(d− 2) 2 − δ; the genus of C. We identify smooth points of Γ with the corresponding points on C. In particular, if P is a smooth point on Γ then the Weierstrass gap sequence at P is considered with respect to C. A smooth point P ∈ Γ is called an (e − 2)-inflection point if i(Γ, T ;P ) = e ≥ 3 where T is the tangent line to Γ at P (cf. Brieskorn–Knörre...