Monotonicity of certain integrals involving gamma distributions and their applications in multiple comparisons

Barlow and Gupta (1969) and Alam (1970) studied the monotonicity of two integrals, involving gamma distributions, that arise in certain ranking and selection problems. In this paper, we shall unify their results by studying the monotonicity of two generalized versions of integrals considered by them. We will also provide applications of derived results in study of certain multiple comparison procedures.     

Adaptive reversible data hiding for JPEG images with multiple two-dimensional histograms

Joint photographic experts group (JPEG) can provide good quality with small file size but also eliminate extensively the redundancies of images. Therefore, hiding data into JPEG images in terms of maintaining high visual quality at small file sizes has been a great challenge for researchers. In this paper, an adaptive reversible data hiding method for JPEG images containing multiple two-dimensional (2D) histograms is proposed. Adaptability is mainly reflected in three aspects. The first one is to preferentially select sharper histograms for data embedding after $K$ histograms are established by constructing the $k$th ($k\in \{1,2,\dots ,K\}$) histogram using the $k$th non-zero alternating current (AC) coefficient of all the quantized discrete cosine transform blocks. On the other hand, to fully exploit the strong correlation between coefficients of one histogram, the smoothness of each coefficient is estimated by a block smoothness estimator so that a sharply-distributed 2D-histogram is constructed by combining two coefficients with similar smoothness into a pair. The pair corresponding to low complexity is selected priorly for data embedding, leading to high embedding performance while maintaining low file size. Besides, we design multiple embedding strategies to adaptively select the embedding strategy for each 2D histogram. Experimental results demonstrate that the proposed method can achieve higher rate–distortion performance which maintaining lower file storage space, compared with previous studies.     

Alkylated indolo[3,2,1-jk]carbazoles as new building blocks for solution processable organic electronics

A facile strategy for the introduction of tert-butyl and hexyl chains to the indolo[3,2,1-jk]carbazole scaffold is presented. With these building blocks six materials based on three different 4,4′-bis(N-carbazolyl)-1,1-biphenyl derivatives with varying degree of planarization were prepared. Characterization of the materials showed that the alkyl chains have only minor effects on the photophysical properties of the compounds. In contrast, thermal robustness towards decomposition and electrochemical stability are increased by the introduced alkyl chains. Detailed investigation of the solubility in five different solvents revealed that the incorporation of the alkyl chains increases the solubility significantly. The increased solubility of the materials allowed the application as host materials in red, green and sky-blue solution processed phosphorescent organic light emitting diodes. Hence, this work presents the first solution processed light emitting devices based on the indolo[3,2,1-jk]carbazole scaffold.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

Exceptionally Plastic/Elastic Organic Crystals of a Naphthalidenimine-Boron Complex Show Flexible Optical Waveguide Properties

The design of molecular compounds that exhibit flexibility is an emerging area of research. Although a fair amount of success has been achieved in the design of plastic or elastic crystals, realizing multidimensional plastic and elastic bending remains challenging. We report herein a naphthalidenimine–boron complex that showed size-dependent dual mechanical bending behavior whereas its parent Schiff base was brittle. Detailed crystallographic and spectroscopic analysis revealed the importance of boron in imparting the interesting mechanical properties. Furthermore, the luminescence of the molecule was turned-on subsequent to boron complexation, thereby allowing it to be explored for multimode optical waveguide applications. Our in-depth study of the size-dependent plastic and elastic bending of the crystals thus provides important insights in molecular engineering and could act as a platform for the development of future smart flexible materials for optoelectronic applications.     

A novel method for crack detection in beam-like structures by measurements of natural frequencies

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.     

Interaction of modulated pulses in nonlinear oscillator chains

We formally derive and rigorously justify the modulation equations of lowest order for the interaction of two modulated pulses on a one-dimensional nonlinear oscillator chain. We show that solutions with the initial form of the assumed ansatz preserve this form over time intervals with positive macroscopic length, and we show a bound on the possible shift of the envelope caused by the interaction. Thus, we rigorously justify and quantify the statement that under the given conditions there is almost no interaction of the modulated pulses.