### in QUALITATIVE RESULTS FOR DISTRIBUTED SYSTEMS WITH DISCRETE DAMPING AND STIFFNESS WITH APPLICATION TO CONTROL, INTERIM SCIENTIFIC REPORT,

, 1984

"... The research carried out under this grant [1] considered the vibration and control of a linear non-conservative dynamic systems described by partial differential equations of the form utt.U,t) + L1ut(x,t) + L2uCx,t) = fCx,t) on Q (1) Bu(x,t) = 0 on 3ft where L-. and L are time invariant ..."

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partial differential operators defined on a

*Hilbert*Space, H, consisting of all appropriately smooth functions satisfying the boundary conditions, Q is a bounded open region in R, n=1,2,*3*, with boundary 8*ft*, t denotes the time, and u(x,t) is the deflection at the position x in*ft*. The subscript t denotes### NONLINEAR ERGODIC THEOREMS FOR FAMILIES OF NONEXPANSIVE MAPPINGS IN BANACH SPACES

"... The filst nonlinear ergodic theorem $\mathrm{f}\mathrm{o}1^{\cdot} $ nonexpallsive nlappings in a Hilbert space was $\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l})\mathrm{l}\mathrm{i}\mathrm{S}\mathrm{h}\mathrm{e}\mathrm{d} $ by Baillon [2]: Let $C1$) $\mathrm{e} $ a nonelllpty closed convex su ..."

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subset of a Hilbelt space and let $T $ be a $\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{X}1^{)\mathrm{a}}$nsive nlapl)ing of $C $ into itself. If the set $

*F(T*) $ of fixed points of $T $ is $\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{l}1^{)}\mathrm{t}_{*3*}r$, then for each $x\in C### Citation

"... Second-order dipolar order in magic-angle spinning nuclear magnetic resonance J. Chem. Phys. 135, 154507 (2011) Single crystal nuclear magnetic resonance in spinning powders J. Chem. Phys. 135, 144201 (2011) Resistive detection of optically pumped nuclear polarization with spin phase transiti ..."

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transition peak at Landau level filling factor 2/

*3*Appl. Phys. Lett. 99, 112106 (2011) High-resolution 13C nuclear magnetic resonance evidence of phase transition of Rb,Cs-intercalated singlewalled nanotubes J. Appl. Phys. 110, 054306 (2011) Distribution of non-uniform demagnetization fields###
Spherically symmetric solutions on non trivial frame in *f(T*) theories of gravity

"... New solution with constant torsion is derived using the field equations of f(T). Asymptotic form of energy density, radial and transversal pressures are shown to met the standard energy conditions. Other solutions are obtained for vanishing radial pressure and physics relevant to the resulting model ..."

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of equation of state and negative pressure[

*3*], etc. It is not clear what type of DE is more seemingly to explain the current era of the universe. A very attractive possibility is the already mentioned as “modification of General Relativity ” (GR). Amendments to the*Hilbert*-Einstein action through### c © 1997 Universitat de Barcelona On Musielak-Orlicz spaces isometric to L2 or L∞

"... It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t)= c(t)u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be is ..."

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It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a

*Hilbert*space coincides with L2 up to a weight, that is Φ(u,t)= c(t)u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ### SOME ERGODIC THEOREMS FOR A FINITE FAMILY OF NONEXPANSIVE MAPPINGS By

, 1982

"... 1. In [1], J. B, Baillon proved the first ergodic theorem for nonlinear mappings jn Hilbert space: Let C be a closed convex bounded subset of a Hilbert space X and Tbe a nonexpansive self-mapping of C, then for each xEC the Cesbro means ili-2:;6Tkx converge weakly to a fixed point of Tas n-År oo. Si ..."

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1. In [1], J. B, Baillon proved the first ergodic theorem for nonlinear mappings jn

*Hilbert*space: Let C be a closed convex bounded subset of a*Hilbert*space X and Tbe a nonexpansive self-mapping of C, then for each xEC the Cesbro means ili-2:;6Tkx converge weakly to a fixed point of Tas n-År oo### ON TIME REGULARITY OF STOCHASTIC EVOLUTION EQUATIONS WITH MONOTONE COEFFICIENTS

"... Abstract. We report on a time regularity result for stochastic evolutionary PDEs with mono-tone coefficients. If the diffusion coefficient is bounded in time without additional space reg-ularity we obtain a fractional Sobolev type time regularity of order up to 1 2 for a certain functional G(u) of t ..."

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*Hilbert*spaces and let V be a Banach space such that V ↪ → H ↪ → V ′ is a Gelfand triple with continuous and dense embeddings. We are interested in stochastic evolution equations of the form du = A(t, u) dt+B(t, u) dW, u(0) = u0, (1.1) where W is a U-valued cylindrical Wiener process on a probability

### U-INVARIANT SAMPLING 1 U-Invariant Sampling: Extrapolation and Causal Interpolation from Generalized Samples

"... Abstract—Causal processing of a signal’s samples is crucial in on-line applications such as audio rate conversion, compression, tracking and more. This paper addresses the problems of predict-ing future samples and causally interpolating deterministic sig-nals. We treat a rich variety of sampling me ..."

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and modulation operators. From an abstract

*Hilbert*-space viewpoint, such sequences of functions were studied extensively in the context of stationary random processes. We thus utilize powerful tools from this discipline, although our problems are deterministic by nature. In particular, we provide necessary