Composition Operators with Universal Translates on S^(2)(D)

It is known that the Invariant Subspace Problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one dimensional.In this paper,we characterize all linear fractional composition operators and their adjoints that have universal translates on the space S^(2)(D).Moreover,we characterize all adjoints of linear fractional composition operators that have universal translates on the Hardy space H^(2)(D).In addition,we consider the minimal invariant subspaces of the composition operator Cφa on S^(2)(D),where φa(z)=az+1-a,a ∈(O,1).Finally,some relationships between complex symmetry and universality for bounded linear operators and commuting pairs of operators on a complex separable,infinite dimensional Hilbert space are explored.

Fuzzy reasoning model based on universal combination operation model

The universal combination operation model is a comprehensive decision model of continuous-valued logic. It overcomes limitations of the scope of operations of reasoning operators in the current comprehensive decision-making system. This article discusses relationship of mutual information and general correlation coefficient and gives the corresponding rules of them, the optimal matching operator is selected to complete fuzzy decision according to mutual information between candidate attributes. The relationship of mutual information between attributes and generalized correlative coefficient provides the principle to select the matching operator. According to the results of experiment, it is more reasonable to enhance classified precision effectively. There is a certain application value of the article＇s method.

Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.

Universal single-mode lasing in fully chaotic two-dimensional microcavity lasers under continuous-wave operation with large pumping power [Invited]

For a fully chaotic two-dimensional(2D) microcavity laser, we present a theory that guarantees both the existence of a stable single-mode lasing state and the nonexistence of a stable multimode lasing state, under the assumptions that the cavity size is much larger than the wavelength and the external pumping power is sufficiently large. It is theoretically shown that these universal spectral characteristics arise from the synergistic effect of two different kinds of nonlinearities: deformation of the cavity shape and mode interaction due to a lasing medium. Our theory is based on the linear stability analysis of stationary states for the Maxwell–Bloch equations and accounts for single-mode lasing phenomena observed in real and numerical experiments of fully chaotic 2D microcavitylasers.

Axiomatization for 1-level universal AND operator

The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system ULh∈（0,1） based on l-level universal AND operator of universal logic is algebra LПIG is introduced. The of system ULh∈（0,1） are proved. built up. The corresponding soundness and the completeness