The purpose of this study is to develop an accelerated MR parameter mapping technique. For accelerated T1 and T2 mapping, spin-echo inversion recovery and multi-echo spin echo pulse sequences were redesigned to perform undersampling along phase encoding direction. The highly missing k-space were then interpolated by using recently proposed annihilating filter based low-rank Hankel matrix approa...

In what follows, the symbol X stands for a real Banach space with norm ‖ · ‖ and (normalized) duality mapping J. Moreover, “continuous” means “strongly continuous” and the symbol “→” (“⇀”) means strong (weak) convergence. The symbol R (R+) stands for the set (−∞,∞) ([0,∞)) and the symbols ∂D, intD, D denote the strong boundary, interior and closure of the set D, respectively. An operator T : X ...

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

Harer has shown that the mapping class group is a virtual duality groupmirroring the work of Borel-Serre on arithmetic groups in semisimple Q-groups. Just as the homology of the rational Tits building provides the dualizing module for any torsion-free arithmetic group, the homology of the curve complex is the dualizingmodule for any torsion-free, finite index subgroup of the mapping class group...

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C → C a contractive mapping (or a weakly contractive mapping), and T : C → C a nonexpansive mapping with the fixed point set F (T ) 6= ∅. Let {xn} be generated by a new composite iterative scheme: yn = λnf(xn)+(1−λn)Txn, xn+1 = (1−βn)yn+βnTyn, (n ≥ 0). It is pr...

and Applied Analysis 3 space X is embedded compactly in space Y and “X ↪→ Y ′′ denote that space X is embedded continuously in space Y. A mapping T : D T X → X∗ is said to be hemicontinuous on X if w − limt→ 0T x ty Tx, for any x, y ∈ X. Let J denote the duality mapping from X into 2 ∗ defined by J x { f ∈ X∗ : (x, f) ‖x‖ · ∥∥f∥∥,∥∥f∥∥ ‖x‖}, x ∈ X, 1.5 where ·, · denotes the generalized duality...

in this paper we get some results and applications for duals and approximate duals of g-frames in hilbert spaces. in particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of hilbert spaces. we also obtain some results for perturbations of approximate duals.

We present a simple unified formula expressing the denominators of normalized R-matrices between fundamental modules over quantum loop algebras type ADE. It has an interpretation in terms representations Dynkin quivers and can be proved way using geometry graded quiver varieties. As by-product, we obtain geometric Kang-Kashiwara-Kim's generalized affine Schur-Weyl duality functor when it arises...

Forest ecosystems are among the largest terrestrial carbon reservoirs on our planet earth thus playing a vital role in global carbon cycle. Presently, remote sensing techniques provide proper estimates of forest biomass and quantify carbon stocks. The present study has explored Landsat-8 sensor product and evaluated its application in biomass mapping and estimation. The specific objectives were...