Hilbert frames theory have been extended to frames in Hilbert $C^*$-modules. The paper introduces equivalent $*$-frames and presents ordinary duals of a constructed $*$-frame by an adjointable and invertible operator. Also, some necessary and sufficient conditions are studied such that $*$-frames and ordinary duals or operator duals of another $*$-frames are equivalent under these conditions. W...

Lüscher established a non-perturbative formula to extract the elastic scattering phases from twoparticle energy spectrum in a torus using lattice simulations. Rummukainen and Gottlieb further extend it to the moving frame, which is devoted to the system of two identical particles. In this work, we generalize Rummukainen-Gottlieb’s formula to the generic two-particle system where two particles a...

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 fram...

Germonpré P, Papadopoulou V, Hemelryck W, Obeid G, Lafère P, Eckersley RJ, Tang M-X, Balestra C. The use of portable 2D echocardiography and ‘frame-based’ bubble counting as a tool to evaluate diving decompression stress. Diving and Hyperbaric Medicine. 2014 March;44(1):5-13.) Introduction: ‘Decompression stress’ is commonly evaluated by scoring circulating bubble numbers post dive using Dopple...

A strong coloring on a cardinal $\kappa$ is function $f:[\kappa]^2\to \kappa$ such that for every $A\subseteq of full size $\kappa$, color $\gamma<\kappa$ attained by $f\upharpoonright[A]^2$. The symbol $\kappa\nrightarrow [\kappa]^2_\kappa$ asserts the existence $\kappa$. We introduce $\kappa\nrightarrow_p[\kappa]^2_\kappa$ which over partition $p:[\kappa]^2\to\theta$. $f$ $p$ if $A\in [\kappa...

OBJECTIVE To explore the use and interpretation of self reported on/off diary data for assessment of daily motor fluctuations in Parkinson's disease. METHODS 26 consecutive non-demented patients with fluctuating Parkinson's disease received standardised training on how to fill out the four category CAPSIT-PD on/off diary, followed by four hours of clinical observation and four weeks of daytim...

in this paper we introduce and study besselian $g$-frames. we show that the kernel of associated synthesis operator for a besselian $g$-frame is finite dimensional. we also introduce $alpha$-dual of a $g$-frame and we get some results when we use the hilbert-schmidt norm for the members of a $g$-frame in a finite dimensional hilbert space.