Quantization of Alternative Hamiltonians

We investigate quantum mechanical implications of canonically inequivalent Hamilton formulations of the Newtonian dynamics. Generated alternative quantizations, being noncanonical, are consistent with the same equations of motion, i.e., they satisfy E.Wigner's principle of quantization. As illustration we consider a noncanonical one-dimensional harmonic oscillator.     

On nonoscillation of canonical or noncanonical disconjugate functional equations

Qualitative comparison of the nonoscillatory behavior of the equations

论庞加莱-契达耶夫方程

研究表明：庞加莱－契达耶夫正则方程是非正则变量下相当普遍的哈密顿方程．这表明，多余坐标下的广义拉格朗日方程和广义哈密顿方程（其阶数低于带有不定乘子的方程），以及准坐标下的欧拉－拉格朗日方程，都是庞加莱－契达耶夫方程的特殊情况；从而，可将其理论推广到上述系统．而且还研讨了庞加莱－契达耶夫方程在非完整系动力学中的应用问题．     

In vivo incorporation of multiple noncanonical amino acids into proteins

Expansion of the standard genetic code enables the design of recombinant proteins with novel and unusual properties. Traditionally, such proteins have contained only a single type of noncanonical amino acid (NCAA) in their amino acid sequence. However, recently reported initial efforts demonstrate that it is possible with suppression-based methods to translate two chemically distinct NCAAs into a single recombinant protein by combining the suppression of different termination codons and nontriplet coding units (such as quadruplets). The possibility of expanding the code with various NCAAs simultaneously further increases the toolkit for the generation of multifunctionalized proteins.     

Genetic Incorporation of a Reactive Isothiocyanate Group into Proteins

Methods for the site‐specific modification of proteins are useful for introducing biological probes into proteins and engineering proteins with novel activities. Herein, we genetically encode a novel noncanonical amino acid (ncAA) that contains an aryl isothiocyanate group which can form stable thiourea crosslinks with amines under mild conditions. We show that this ncAA (pNCSF) allows the selective conjugation of proteins to amine‐containing molecular probes through formation of a thiourea bridge. pNCSF was also used to replace a native salt bridge in myoglobin with an intramolecular crosslink to a proximal Lys residue, leading to increased thermal stability. Finally, we show that pNCSF can form stable intermolecular crosslinks between two interacting proteins.     

Wavelet Image Compressor—MinImage

Nowadays, still images are used everywhere in the digital world. The shortages of storage capacity and transmission bandwidth make efficient compression solutions essential. A revolutionary mathematics tool, wavelet transform, has already shown its power in image processing. MinImage, the major topic of this paper, is an application that compresses still images by wavelets. MinImage is used to compress grayscale images and true color images. It implements the wavelet transform to code standard BMP image files to LET wavelet image files, which is defined in MinImage. The code is written in C++ on the Microsoft Windows NT platform. This paper illustrates the design and implementation details in Min-Image according to the image compression stages. First, the preprocessor generates the wavelet transform blocks. Second, the basic wavelet decomposition is applied to transform the image data to the wavelet coefficients. The discrete wavelet transforms are the kernel component of MinImage and are discussed in detail. The different wavelet transforms can be plugged in to extend the functionality of MinImage. The third step is the quantization. The standard scalar quantization algorithm and the optimized quantization algorithm, as well as the dequantization, are described. The last part of MinImage is the entropy-coding schema. The reordering of the coefficients based on the Peano Curve and the different entropy coding methods are discussed. This paper also gives the specification of the wavelet compression parameters adjusted by the end user. The interface, parameter specification, and analysis of MinImage are shown in the final appendix.     

Screening of Minimalist Noncanonical Sites in Duplex DNA and RNA Reveals Context and Motif-Selective Binding by Fluorogenic Base Probes

We hypothesize that programmable hybridization to noncanonical nucleic acid motifs may be achieved by macromolecular display of binders to individual noncanonical pairs (NCPs). As each recognition element may individually have weak binding to an NCP, we developed a semi-rational approach to detect low affinity interactions between selected nitrogenous bases and noncanonical sites in duplex DNA and RNA. A set of fluorogenic probes was synthesized by coupling abiotic (triazines, pyrimidines) and native RNA bases to thiazole orange (TO) dye. This probe library was screened against duplex nucleic acid substrates bearing single abasic, single NCP, and tandem NCP sites. Probe engagement with NCP sites was reported by 100–1000× fluorescence enhancement over background. Binding is strongly context-dependent, reflective of both molecular recognition and stability: less stable motifs are more likely to bind a synthetic probe. Further, DNA and RNA substrates exhibit entirely different abasic and single NCP binding profiles. While probe binding in the abasic and single NCP screens was monotonous, much richer binding profiles were observed with the screen of tandem NCP sites in RNA, in part due to increased steric accessibility. In addition to known binding interactions between the triazine melamine (M) and T/U sites, the NCP screens identified new targeting elements for pyrimidine-rich motifs in single NCPs and 2×2 internal bulges. We anticipate that semi-rational approaches of this type will lead to programmable noncanonical hybridization strategies at the macromolecular level.