Abstract:
In this note, we prove the Kazdan's inequalities without using what is called the Heisenberg uncertainty principle. Instead we prove it using Garofalo-Lin inequality among other things.

Abstract:
In this paper we attempt to prove Lehmer's conjecture on Ramanujan's tau function, namely tau(n) is never zero, for each n larger than zero by investigating the additive group structure attached to tau(n) with the aid of unique factorization theorem.

Abstract:
In this paper we prove Lehmer's conjecture on Ramanujan's tau function, namely tau(n) not equal to zero for n >= 1 by investigating the additive group structure attached to tau(n) with the aid of the pigeonhole principle and unique factorization theorem.

Abstract:
This study investigates the response frequency conversion characteristic of a nonlinear curved panel mounted with a centre mass and the sound radiations. A set of coupled governing differential equations is set up and used to generate the nonlinear vibration responses, which are used to calculate the corresponding radiated sounds. The vibration, sound levels, and the ratio of the antisymmetrical to symmetrical mode responses are plotted against the excitation level and compared with a set of experimental data. The frequency conversion characteristic is investigated from the frequency spectrums of the vibration responses.

Abstract:
This paper presents a privacy-preserving path-authentication method for supply chain management using RFID. Compared with previous works, our scheme employs only symmetric encryption and message authentication codes. This reduces computation and communication overhead. The proposed method also supports high-level privacy without the need for tamper-proof tags as compared with the previous methods. Performance analysis demonstrates that the proposed scheme requires far less computation resource than recent works, proving that less than 1 minute is enough to verify 100000 RFIDs in a conventional reader environment.

Abstract:
The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. The results obtained from the harmonic balance and homotopy perturbation approaches verified each other. The effects of vibration amplitude, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth, on the first two resonant natural frequencies, are examined. 1. Introduction Over the past decades, many researchers worked on linear structural-acoustic research works (e.g., [1–7]) and nonlninear structural vibration problems (e.g., [8–15]), separately. The structural-acoustic problem of rectangular tube (or similar problems) has been studied for many years in various studies. So far, only few research works about structural-acoustics have adopted the assumption of large amplitude vibration [16–20]. Few classical solutions for nonlinear structural-acoustic problems have been developed to date, although there are many approaches available for solving nonlinear governing differential equation (e.g., [21–30]. In the study reported in this paper, the homotopy perturbation and harmonic balance methods are used and assessed. It is because these two methods were employed to determine the large amplitude free vibration of beams and nonlinear oscillators in previous studies and agreed well with the other published results [31]. The results obtained from these two methods verified each other. In finite element and other numerical approaches for solving the problems of nonlinear structural vibrations (e.g., [32–35]), it is necessary for setting a set of residual equations or global matrix equations and then solving them for the eigenvalue solutions. All these approaches require a significant effort as an eigenvalue problem. The present study uses the multiacoustic and single structural mode approach to develop the classical solutions which do not require a significant amount of computational effort and preprocessing inputs. 2. Theory 2.1. Governing Equations In Figure 1, the acoustic pressure within the rectangular tube induced by the flexible end is given by the following homogeneous wave equation [1]: where P = the pressure within the tube; τ = time; = sound speed. Figure 1: The rectangular tube with one open end, one flexible end, and

Study Objective: We studied the overall efficacy of fiberoptic aided intubation using three different supraglottic airways (SGA) as intubation conduits with a standard endotracheal tube (ETT) to determine which, if any, is superior as an intubation conduit. Design: After induction of general anesthesia, subjects were randomized to one of three groups: Air-Q ILA^{TM}, LMA Classic Excel^{TM}, and LMA Unique^{TM}. Subjects were intubated with a fiberoptic aided technique with continuous ventilation with FiO_{2} = 1.0 through one of these SGAs. The primary endpoint was the overall efficacy of the intubation procedure. In addition, the following data were collected: demographic data, intubation times, grade of view of the larynx, and a visual analog scale (VAS) score of difficulty as determined by the primary anesthesiologist performing the procedure. Data were analyzed using a Kruskal-Wallis one-way analysis of variance and Post hoc analysis was done using Dunn’s Multiple Comparison Test. Results: 126 total subjects were studied. Intubation success rates were 100%, 87.8%, and 95% with the Air-Q ILA^{TM}, LMA Classic Excel^{TM}, and LMA Unique^{TM} respectively. There was no significant difference among the three different SGAs when comparing the times to place the SGA (T1), the true intubating time (T2), the time to remove the SGA (T3), or the total time (T4). Data were also stratified by the grade of view of the larynx; all grade I views, grade II views, and grade III views were grouped together regardless of the type of the SGA used. The grade I view of the larynx group had significantly faster true intubation times (T2 = 75.1 sec, p = 0.01) and significantly lower VAS scores (VAS = 1.9, P = < 0.0001) when compared to both the grade II views (T2= 92.7 sec, VAS = 3.2) and grade III views (T2 = 111.6 sec, VAS = 4.9). Conclusions: We conclude that the Air-Q ILA^{TM} provides the best view of the larynx and is the easiest one to use as an intubation conduit.

Abstract:
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately determining the transmission probabilities as well as the wave function in both classically accessible region and inaccessible region for any barrier potentials. It is also shown that the energy eigenvalues and the wave functions of bound states can be obtained for potential-well structures by exploiting this method. Calculational results of illustrative examples are shown in order to verify this method for treating barrier and potential-well problems.