On the second eigenvalue of the Laplace operator on a spherical band

In this paper we prove that the second eigenvalue of the Laplacian for a spherical band on the unit sphere has multiplicity 2. We also show that among all spherical bands of given fixed area less than the second eigenvalue is maximized at the band which is symmetrical with respect to the equator.

     

The unusual paramagnetic mixed-metal carbonyl chalcogenide clusters: [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te,Se)

The rare examples of electron-rich mixed-metal carbonyl telluride and selenide clusters [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te, Se) have been demonstrated. These two novel carbonyl complexes exhibit the unusual paramagnetic behavior.     

An investigation on dispersion of carbon nanotubes in chitosan aqueous solutions

The dispersion of carbon nanotubes (CNT) in water of different pH and in chitosan aqueous solution of three acids, acetic acid, formic acid, and hydrochloric acid, was investigated. Chitosan was soluble in water of pH ≤3 and could well disperse untreated CNT and acid-treated CNT, both of which had poor dispersion in water of pH ≤3. With the presence of 0.1 wt% chitosan in solution, particle sizes of the CNT dispersion were found to decrease with increasing COOH contents on the CNT. Particle sizes of CNT, untreated and acid-treated, in the three acidic aqueous solutions were found to increase with increasing chitosan contents in solutions. Among the three acids, hydrochloric acid gave the smallest particle size of the CNT dispersion. Without chitosan, the dispersibility of the acid-treated CNT in aqueous solutions of three acids was in the order of acetic acid > formic acid > hydrochloric acid.     

Effects of carbon nanotubes on dynamic mechanical property,thermal property,and crystal structure of poly(L‐lactic acid)

Effects of carbon nanotubes (CNT) on the dynamic mechanical property, thermal property, and crystal structure of poly(L ‐lactic acid) (PLLA) were investigated. Dynamic mechanical analysis (DMA) found that CNT via grafting modification with PLLA (CNT‐g‐PLLA) could result in effective reinforcing effects. Tan δ of DMA found that CNT‐g‐PLLA was compatible with the PLLA matrix, giving a single T_g of the composite with a higher CNT‐g‐PLLA loading giving a higher T_g of the composite. Wide angle X‐ray diffraction (WAXD) data demonstrated that CNT could assist the disorder‐to‐order (α′‐to‐α) transition in PLLA crystals but did not lead to a more compact chain packing of the crystal lattice in PLLA composites than in pure PLLA. The equilibrium melting temperature (T) obtained from Hoffman‐Weeks plots were found to increase with increasing CNT‐g‐PLLA content. Small angle X‐ray scattering data revealed that thicknesses of crystal layer and amorphous layer of PLLA both decreased with increasing CNT contents. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 145–152, 2010     

Optical phase modulators using deformable waveguides actuated by micro-electro-mechanical systems

An optical phase modulator is presented by using micro-electro-mechanical systems to actuate deformable silicon waveguides. Via mechanically stretching the waveguide length, the optical path is extended, resulting in a phase shift. The experimental results show that a phase shift of near 0.4π is achieved at 200 V for both TE- and TM-polarized waves by cascading six phase modulation units, agreeing well with the theoretical prediction. The power consumption is estimated to be smaller than 0.2 mW at 200 V, mainly resulting from the leakage current.     

Synchronization of the chaotic secure communication system with output state delay

In this paper, we utilize a proper Lyapunov function and Lyapunov theorem, combined with LMIs method, in order to design a controller L, which ensures the synchronization between the transmission and the reception ends of the chaotic secure communication system with time-delay of output state. Meanwhile, for the purpose of increasing communication security, we encrypt and decrypt the original to-be-transmitted message with the techniques of n-shift cipher and public key. The result of simulation shows that the proposed method is able to synchronize the transmission and the reception ends of the system, and moreover, to recover the original message at the reception end. Therefore, the method proposed in this paper is effective and feasible to apply in the chaotic secure communication system.     

Inverse nodal and inverse spectral problems for discontinuous boundary value problems

Inverse nodal and inverse spectral problems are studied for second-order differential operators on a finite interval with discontinuity conditions inside the interval. Uniqueness theorems are proved, and a constructive procedure for the solution is provided.     

Model conversions of uncertain linear system using the improved block-pulse function approach

This paper presents an improved block-pulse function approach to convert a continuous-time (respectively, discrete-time) structured uncertain linear system into an equivalent discrete-time (respectively, continuous-time) structured uncertain linear model. The concept of the principle of equivalent areas is utilized for the uncertain model conversions. This allows the use of well-established theorems and algorithms in the discrete-time (respectively, continuous-time) domain to indirectly solve the continuous-time (respectively, discrete-time) domain problems. A numerical example is given to demonstrate the effectiveness of the proposed method.     

Hybrid control for synchronizing a chaotic system

In this paper, a hybrid control based on pulse width modulator (PWM) is proposed to synchronize a class of master–slave chaotic systems with uncertainties. We use the Genetic Algorithm (GA) together with fuzzy logic to tune the switching time of PWM mode controller such that the output response of master–slave chaotic system can be synchronized. Finally, an example, uncertain master–slave Duffing–Holmes chaos system, is proposed to show the proposed method’s effectiveness for chaotic synchronization.