Shockwave Visualization Using Holographic Interferometer

High-speed holographic interferometry was employed to visualize and record Shockwave phenomena. We performed three kinds of holographic interferometry for visualization and recording of the propagation of a Shockwave: a real-time holographic interferometer with a high-speed framing camera, a real-time holographic interferometer with a high-speed streak camera and a double-pulse laser holographic interferometer with a dual-reference-beam module. The experimental results were compared and their advantages and disadvantages are discussed. The experimental results clearly show the high-speed Shockwave propagation and give the feasibility of quantitative interpretation of high-speed gas-dynamics.     

ZSM-5沸石结晶度对乙苯叔丁基化对位选择性的影响(英文)

Highly crystalline ZSM-5 zeolites are important for para-selective alkylation of alkyl aromatics, because they carry few external acid sites for isomerization of p-dialkyl products. Such zeolites (Si/Al = 25, 50, and 75) were synthesized in a fluoride medium between pH 4 and 6. Their crystallinities, crystal sizes, and surface areas were higher than those of a commercial ZSM-5 zeolite. Their para selectivities in alkylation were tested for vapor-phase tert-butylation of ethylbenzene between 200 and 400 °C. As expected, all the catalysts showed more than 90% para selectivity. At 300 °C, ethylbenzene conversion decreased in the order ZSM-5(25, commercial) > ZSM-5(25) > ZSM-5(50) > ZSM-5(75). The catalysts had weak, medium, and strong acid sites, but all the acid sites of ZSM-5(75) were weaker than those of ZSM-5(25) and ZSM-5(50). The high activity of commercial ZSM-5 was caused by its strong acid sites being stronger than those of the synthesized zeolites. Although the activity of the commercial catalyst was higher than those of the present catalysts, the selectivity for 4-t-butylethylbenzene (4-t-BEB) was low. The optimum feed ratio (ethylbenzene:t-butyl alcohol) was 2:1 and the feed rate was 1.65 h?1 for high ethylbenzene conversion and 4-t-BEB selectivity. Time-on-stream studies showed slow catalyst deactivation. Highly crystalline ZSM-5 zeolites are therefore better than a commercial zeolite for para-selective alkylation of alkyl aromatics. They do not require much post-modification for high para selectivity. A fluoride medium is therefore better than an alkaline medium for obtaining highly crystalline para-selective ZSM-5 zeolites.     

On the stability of a cubic functional equation

In this paper, we will find out the general solution and investigate the generalized Hyers-Ulam-Rassias stability problem for the following cubic functional equation
2f（x ＋ 2y） ＋ f（2x - y） = 5f（x ＋ y） ＋ 5f（x - y）＋ 15f（y）
in the spirit of Hyers, Ulam, Rassias and Gavruta.     

HYERS—ULAM—RASSIAS STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A C^＊—ALGEBRA

The authors prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital C*-algebra, and prove the Hyers-Ulam-Rassias stability of the quadratic mapping in Banach modules over a unital Banach algebra.     

SOUND TRANSMISSION THROUGH ELASTOMERIC BULB SEALS

The sound barrier performance of elastomeric vehicle weather seals was investigated. Experiments were performed on a single bulb seal specimen using a reverberation room method. The seal wall velocity was measured using a laser Doppler vibrometer. The sound pressure near the velocity measurement location was measured simultaneously, which allowed the sound intensity on both sides of the seal and the sound transmission loss to be determined. The vibration response and the sound transmission loss of the bulb seal were then computed using finite element analysis. Acoustic-structure interactions were considered for a partially coherent spatially distributed pressure excitation. The experimental data obtained using the reverberation room method allowed the validation of the numerical models. The resonance frequency due to the mass-air-mass mode of vibration was accurately predicted. The model was then used to numerically investigate the influence of various design parameters. It was found that the elastic modulus significantly affects the bulb seal resonance frequency, and that the loss factor of the material has major effects on the sound transmission loss around resonance.     

Quadratic double centralizers and quadratic multipliers

In this paper, we establish stability of quadratic double centralizers and quadratic multipliers on Banach algebras. We also prove the super stability of quadratic double centralizers on Banach algebras which are weakly commutative and weakly without order, and of quadratic multipliers on Banach algebras which are weakly without order.     

Isomorphisms, derivations and isometries in proper CQ*-algebras

In this paper, we investigate homomorphisms in proper CQ-algebras, proper Lie CQ-algebras and proper Jordan CQ-algebras and deriva-tions on proper CQ-algebras, proper Lie CQ-algebras and proper JordanCQ-algebras associated with the Cauchy-Jensen functional equation2f(x + y2+ z)= f(x) + f(y) + 2f(z);which was introduced and investigated in [3, 28].Furthermore, Isometries and isometric isomorphisms in proper CQ-algebrasare studied.     

Multivalued fixed point in Banach algebra using continuous selection and its application to differential inclusion

In this paper, we provide some fixed point results using continuous selection given by Poonguzali et al. [15]. Also, using the selection theorem we discusse the existence of fixed point for the product of two multivalued mappings, that is, of the form $Ax\cdot Bx.$ Using those fixed point results, we give the existence of solution for a newly developed differential inclusion.     

Isometric isomorphisms in proper <Emphasis Type="Italic">CQ</Emphasis>*-algebras

In this paper, we prove the Hyers-Ulam-Rassias stability of isometric homomorphisms in proper CQ＊-algebras for the following Cauchy-Jensen additive mapping： 2f[（x1＋x2）/2＋y]=f（x1）＋f（x2）＋2f（y） The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias＇ stability theorem that appeared in the paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 （1978）, 297-300. This is applied to investigate isometric isomorphisms between proper CQ＊-algebras.