Uncomplemented subspaces of Lorentz spaces

In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000.     

Emittance measurement & optimization for the photocathode RF gun with laser profile shaping

The Laser Undulator Compact X-ray source(LUCX) is a test bench for a compact high brightness X-ray generator,based on inverse Compton Scattering at KEK,which requires high intensity multi-bunch trains with low transverse emittance.A photocathode RF gun with emittance compensation solenoid is used as an electron source.Much endeavor has been made to increase the beam intensity in the multi-bunch trains.The cavity of the RF gun is tuned into an unbalanced field in order to reduce space charge effects,so that the field gradient on the cathode surface is relatively higher when the forward RF power into gun cavity is not high enough.A laser profile shaper is employed to convert the driving laser profile from Gaussian into uniform.In this research we seek to find the optimized operational conditions for the decrease of the transverse emittance.With the uniform driving laser and the unbalanced RF gun,the RMS transverse emittance of a 1 nC bunch has been improved effectively from 5.46 πmm.mrad to 3.66 πmm.mrad.     

Reconstruction of Hp -Functions: Best Approximation,Regularization and Optimal Error Estimates

Let U be the open unit disc of the complex plane. We explicitly construct the best pointwise approximation for determining a function in the Hardy space H ^p (U) from measured data at a countable set of points in U whenever the data is exact. A regularization scheme is given to deal with the case of nonexact data. Moreover, optimal error estimates are also studied.     

On the Newton-Kantorovich method inK-normed spaces

Nondifferentiable operator equations in spaces equipped with aK-norm — map taking values in the cone of an ordered Banach space — are studied. The majorant method is used to derive the convergence of a modified sequence of Newton-Kantorovich approximations.     

Power Spectrum in Krein Space Quantization

The power spectrum of scalar field and space-time metric perturbations produced in the process of inflation of universe, have been presented in this paper by an alternative approach to field quantization namely, Krein space quantization (Gazeau et al. in Class. Quantum Gravity 17:1415, 2000; Takook in Int. J. Mod. Phys. E 11:509, 2002; Rouhani and Takook in ). Auxiliary negative norm states, the modes of which do not interact with the physical world, have been utilized in this method. Presence of negative norm states play the role of an automatic renormalization device for the theory.     

On Picard iterations for strongly accretive and strongly pseudo-contractive Lipschitz mappings

In this note, we speed up the convergence of the Picard sequence of iterations for strongly accretive and strongly pseudo-contractive mappings. Our results improve the results of Chidume [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint no. IC2000098; C.E. Chidume, Iterative Algorithms for Non-expansive Mappings and Some of Their Generalizations, in: Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, vol. 1, 2, Kluwer Acad. Publ, Dordrecht, 2003, pp. 383–429], and Liu [L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Amer. Math. Soc. 125 (2) (1997) 1363–1366], and some other known results. The technique of the proof, presented in this paper, is different from the technique used by Chidume.     

On small homotopies of loops

Two natural questions are answered in the negative:

• “If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic?”

• “Can adding arcs to a space cause an essential curve to become nulhomotopic?”

The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and π₁-shape injective.

Numerical algorithm for parabolic problems with non-classical conditions

The parabolic problems with non-classical conditions are discussed in a reproducing kernel space in this paper. A reproducing kernel space is constructed, in which the non-classical conditions of the parabolic problems are satisfied. Based on the reproducing kernel space, a new technique for solving the non-classical parabolic problems is presented. Some examples are displayed to demonstrate the validity and applicability of the proposed method.     

On positive invertibility of operators and their decompositions

In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U^–1 exists, VU^–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU^–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU^–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)