Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Ionization thresholds and positions of avoided crossing of potassium Stark Rydberg states: a Stark-adapted quantum defect orbital treatment

We have calculated the positions of the avoided level crossings between (n+2)s, np states and nd, k Stark states in the Rydberg Stark states of the potassium atom with principal quantum number n comprised between 12 and 17. We have also studied the adiabatic electric field ionization thresholds for the above Rydberg states. Both the ionization thresholds and the positions of avoided crossings have been calculated using the recently developed Stark-adapted quantum defect orbital (SQDO) formalism. The presently reported values appear to be in very good agreement with the available theoretical and experimental data.     

基于拉曼光谱法的降糖类药物的判别方法比较

采用了四种聚类方法对降糖类药物拉曼光谱进行了快速、无损判别。采集九种降糖类药品共48个样品的拉曼光谱,经截波、基线校正、平滑、矢量归一化等预处理后,分别采用K-均值、系统聚类法、自组织图(SOM)及PCA-SOM四种不同聚类方法做聚类判别。结果表明,自组织图与K-均值、系统聚类法相比,聚类结果较好,并且SOM结合PCA后的PCA-SOM结果最优。为降糖类药品的快速判别从聚类的角度提供了一种新的方法。     

On the Discrete Criteria and JØ rgensen Inequalities for SL(m,F((t)))

In this paper, the author gives the discrete criteria and J\o rgensen inequalities of subgroups for the special linear group on $\overline{\mathrm{F}}((t))$ in two and higher dimensions.     

Explicit–implicit mapping approach to nonlinear blind separation of sparse nonnegative dependent sources from a single mixture: pure component extraction from nonlinear mixture mass spectra

The nonlinear, nonnegative single‐mixture blind source separation problem consists of decomposing observed nonlinearly mixed multicomponent signal into nonnegative dependent component (source) signals. The problem is difficult and is a special case of the underdetermined blind source separation problem. However, it is practically relevant for the contemporary metabolic profiling of biological samples when only one sample is available for acquiring mass spectra; afterwards, the pure components are extracted. Herein, we present a method for the blind separation of nonnegative dependent sources from a single, nonlinear mixture. First, an explicit feature map is used to map a single mixture into a pseudo multi‐mixture. Second, an empirical kernel map is used for implicit mapping of a pseudo multi‐mixture into a high‐dimensional reproducible kernel Hilbert space. Under sparse probabilistic conditions that were previously imposed on sources, the single‐mixture nonlinear problem is converted into an equivalent linear, multiple‐mixture problem that consists of the original sources and their higher‐order monomials. These monomials are suppressed by robust principal component analysis and hard, soft, and trimmed thresholding. Sparseness‐constrained nonnegative matrix factorizations in reproducible kernel Hilbert space yield sets of separated components. Afterwards, separated components are annotated with the pure components from the library using the maximal correlation criterion. The proposed method is depicted with a numerical example that is related to the extraction of eight dependent components from one nonlinear mixture. The method is further demonstrated on three nonlinear chemical reactions of peptide synthesis in which 25, 19, and 28 dependent analytes are extracted from one nonlinear mixture mass spectra. The goal application of the proposed method is, in combination with other separation techniques, mass spectrometry‐based non‐targeted metabolic profiling, such as biomarker identification studies. Copyright © 2015 John Wiley & Sons, Ltd.     

Channel capacities via p-summing norms

In this paper we show how the metric theory of tensor products developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in Shannon's information theory. Furthermore, in the last years Shannon's theory has been fully generalized to the quantum setting, and revealed qualitatively new phenomena in comparison. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. These capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. Our approach to restricted capacities is based on tools from functional analysis, and in particular the notion of p  -summing maps going back to Grothendieck's work. Pisier's noncommutative vector-valued _Lp$L_p$ spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting.     

Non-integrability vs. integrability in pentagram maps

We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective duality. We show that in many cases the pentagram map cannot be included into integrable flows as a time-one map, and discuss how the corresponding notion of discrete integrability can be extended to include jumps between invariant tori. We also present a numerical evidence that certain generalizations of the integrable 2D pentagram map are non-integrable and present a conjecture for a necessary condition of their discrete integrability.     

Comparison of criteria used to access carcinogenicity in CPANN QSAR models versus the knowledge-based expert system Toxtree

The primary goal of this study was to describe and compare the criteria used to assess carcinogenic activity. The statistically-based predictive quantitative structure–activity relationship (QSAR) models based on the counter propagation artificial neural network (CPANN) algorithm, and knowledge-based expert systems based on a decision tree structural alert (SA) approach (Toxtree application), were considered. The integration of the QSAR (CPANN models) and SAR (Toxtree SA application) approach contributed to the mechanistic understanding of the QSAR model considered. The mapping technique inherent to CPANN Kohonen enables us to relate the similarities or dissimilarities within a congeneric set of chemicals with particular SAs for carcinogenicity. The focus of our investigations was the similarities and dissimilarities of the features used in the QSAR and SAR methods. Due to the complexity of the carcinogenic endpoint, the integration of different approaches allows the models to be improved and provides a valuable technique for evaluating the safety of chemicals.