Let $X$ be a  Banach  space, $Csubset X$  be  a  closed  convex  set  included  in  a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a  bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set  $C$,  so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...

In this paper we proved that every g-Riesz basis for Hilbert space $H$ with respect to $K$ by adding a condition is a Riesz basis for Hilbert $B(K)$-module $B(H,K)$. This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual fra...

MRI is an unusual medical imaging modality in that the raw data used to form an image can be collected in an infinite number of ways. While conventional Cartesian k-space scanning is by far the most common scanning method, non-Cartesian approaches have shown promise for rapid imaging, motion robustness, ultrashort TE imaging, rapid spectroscopic imaging, and other applications. A key component ...

A pseudo-random, velocity-insensitive, volumetric k-space sampling trajectory is designed for use with balanced steady state imaging. Individual arcs are designed independently and do not fit together in the way that multi-shot spiral, radial or echo-planar trajectories do. Previously, it was shown that second-order cone optimization problems can be defined for each arc independent of the other...

We present a k-space approximation that directly relates a pulse sequence to its residual pattern of z-directed magnetization M(z), in a manner akin to the k-space approximation for small tip-angle excitation. Our approximation is particularly useful for the analysis and design of tagging sequences, in which M(z) is the important quantity-as opposed to the transverse magnetization components M(...

The k-DNF resolution proof systems are a family of systems indexed by the integer k, where the k member is restricted to operating with formulas in disjunctive normal form with all terms of bounded arity k (k-DNF formulas). This family was introduced in [Krajı́ček 2001] as an extension of the wellstudied resolution proof system. A number of lower bounds have been proven on k-DNF resolution proof...

Recent results by Dinur et al. (2012) and Austrin et al. (2013) have improved the time-space tradeoff curve for SubsetSum. We analyze a family of hash functions previously introduced by Dietzfelbinger, and apply it to decompose arbitrary k-Sum instances into smaller ones. This allows us to extend the aforementioned tradeoff curve to the k-Sum problem, which is SubsetSum restricted to sets of si...

Supporting top-k document retrieval queries on general text databases, that is, finding the k documents where a given pattern occurs most frequently, has become a topic of interest with practical applications. While the problem has been solved in optimal time and linear space, the actual space usage is a serious concern. In this paper we study various reduced-space structures that support top-k...