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We show that the character SPACE of the VECTOR-valued Lipschitz algebra Lipa (X, E) of order, is homeomorphic to the cartesian product X×ME in the product topology, where X is a compact metric SPACE and E is a unital commutative Banach algebra. We also characterize the form of each character on Lipa (X, E).By appealing to the injective tensor product, we then identify the character SPACE of the VECTOR-valued polynomial Lipschitz algebra LipaP(X, E), generated by the polynomials on the compact SPACE XÍCn. It is also shown that LipaP(X, E) is the injective tensor product LipaP(X, E)ÄÙÎE. Finally, we characterize the form of each character on LipaP(X, E).

In this paper, we study fuzzy substructures in connection with Hv -structures. The original idea comes from geometry, especially from the two dimensional Euclidean VECTOR SPACE. Using parameters, we obtain a large number of hyperstructures of the group-like or ring-like types. We connect, also, the mentioned hyperstructures with the theta-operations to obtain more strict hyperstructures, as Hv -groups or Hv-rings (the dual ones).

SPACE VECTOR Current Regulators (SPCR) have low harmonic currents in steady state, but they have slower transient response compared to other control methods such as hysteresis current regulator. In this paper a new method is proposed to improve transient response of SPCR compared to conventional methods. The proposed technique is based on adjustment of zero VECTOR time intervals and modifying the current regulator PI controller output. The proposed method is used in transients. In steady state, the conventional SPCR method is used. The proposed technique can be applied to existing SPCR systems with no change in the hardware and minimum changes in the DSP software. Simulation results indicate that with the proposed method, the magnitude of current error is reduced compared to the conventional SPCR method. The performance of the proposed method is verified experimentally with a laboratory setup using Texas Instruments TMS320F2407A Digital Signal Processor (DSP) and tested on a 1.5 KW induction motor.

The ”massless” VECTOR field equation in de Sitter (dS) 4-dimensional SPACE is gauge invariant under some special gauge transformations. It is also gauge invariant in ambient SPACE notations in which the field equation is written in terms of the Casimir operators of dS group. In this paper the "massless" VECTOR field equation has been solved in the physical case. It has been shown that the solution can be written as the multiplication of a generalized polarization VECTOR and a ”massless” conformally coupled scalar field in the ambient SPACE notations. The physical VECTOR twopoint function has been calculated using ambient SPACE formalism and its zero curvature limit has been considered. It is shown that the physical VECTOR two-point can be written in terms of the conformally coupled massless scalar two-point function in the ambient SPACE notations. The two-point function is expressed in terms of dS intrinsic coordinates from its ambient SPACE counterpart, which is dS-invariant and is free from any divergences.