Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions

One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.     

Kaplansky Classes and Cotorsion Theories of Complexes

In this article we provide arguments for constructing Kaplansky classes in the category of complexes out of a Kaplansky class of modules. This leads to several complete cotorsion theories in such categories. Our method gives a unified proof for most of the known cotorsion theories in the category of complexes and can be applied to the category of quasi-coherent sheaves over a scheme as well as the category of the representations of a quiver.     

Internal Flow Analysis for Slow Moving Small Droplets in Contact with Hydrophobic Surfaces

Internal fluid flow behavior for slow moving small droplets in contact with hydrophobic surfaces is analyzed. The shape of the droplet is first computed using the Young-Laplace equation. For this purpose a Finite Element (FE) model [1], in which contact constraints are enforced through Penalty and Augmented Lagrange Multiplier methods, is used. The flow field within the droplet is then analyzed using the Stokes flow model, considering a de-coupled approach. Similar to the membrane deformation model, the formulation for the flow analysis is also expressed in the framework of FE analysis. Both, stabilized (Pressure Stabilizing/Petrov-Galerkin PSPG) and Galerkin FE formulations are considered. The motion of the fluid inside the droplet is governed by the slip condition enforced on the membrane of the droplet. Numerical examples for droplets rolling steadily are presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural determination of atricins A and B, new triterpenes from Perovskia atriplicifolia, by 1D and 2D NMR spectroscopy

Atricins A (1) and B (2), two new oleanane-type triterpenes have been isolated from the chloroform-soluble fractions of Perovskia atriplicifolia and their structures assigned from (1)H and (13)C-NMR spectra, Distortion Enhancement by Polarization Trasfer (DEPT) and by 2D-COSY, HMQC, Nuclear Overhauser Enhancement Spectroscopy (NOESY) and Hetronuclear mutiple-bond correlation (HMBC) experiments.     

Investigating Bacterial Volatilome for the Classification and Identification of Mycobacterial Species by HS-SPME-GC-MS and Machine Learning

Species of Mycobacteriaceae cause disease in animals and humans, including tuberculosis and leprosy. Individuals infected with organisms in the Mycobacterium tuberculosis complex (MTBC) or non-tuberculous mycobacteria (NTM) may present identical symptoms, however the treatment for each can be different. Although the NTM infection is considered less vital due to the chronicity of the disease and the infrequency of occurrence in healthy populations, diagnosis and differentiation among Mycobacterium species currently require culture isolation, which can take several weeks. The use of volatile organic compounds (VOCs) is a promising approach for species identification and in recent years has shown promise for use in the rapid analysis of both in vitro cultures as well as ex vivo diagnosis using breath or sputum. The aim of this contribution is to analyze VOCs in the culture headspace of seven different species of mycobacteria and to define the volatilome profiles that are discriminant for each species. For the pre-concentration of VOCs, solid-phase micro-extraction (SPME) was employed and samples were subsequently analyzed using gas chromatography–quadrupole mass spectrometry (GC-qMS). A machine learning approach was applied for the selection of the 13 discriminatory features, which might represent clinically translatable bacterial biomarkers.     

Real‐Time Interrogation of Aspirin Reactivity,Biochemistry, and Biodistribution by Hyperpolarized Magnetic Resonance Spectroscopy

Hyperpolarized magnetic resonance spectroscopy enables quantitative, non‐radioactive, real‐time measurement of imaging probe biodistribution and metabolism in vivo. Here, we investigate and report on the development and characterization of hyperpolarized acetylsalicylic acid (aspirin) and its use as a nuclear magnetic resonance (NMR) probe. Aspirin derivatives were synthesized with single‐ and double‐¹³C labels and hyperpolarized by dynamic nuclear polarization with 4.7 % and 3 % polarization, respectively. The longitudinal relaxation constants (T₁) for the labeled acetyl and carboxyl carbonyls were approximately 30 seconds, supporting in vivo imaging and spectroscopy applications. In vitro hydrolysis, transacetylation, and albumin binding of hyperpolarized aspirin were readily monitored in real time by ¹³C‐NMR spectroscopy. Hyperpolarized, double‐labeled aspirin was well tolerated in mice and could be observed by both ¹³C‐MR imaging and ¹³C‐NMR spectroscopy in vivo.     

Real‐Time Interrogation of Aspirin Reactivity,Biochemistry, and Biodistribution by Hyperpolarized Magnetic Resonance Spectroscopy

Hyperpolarized magnetic resonance spectroscopy enables quantitative, non‐radioactive, real‐time measurement of imaging probe biodistribution and metabolism in vivo. Here, we investigate and report on the development and characterization of hyperpolarized acetylsalicylic acid (aspirin) and its use as a nuclear magnetic resonance (NMR) probe. Aspirin derivatives were synthesized with single‐ and double‐¹³C labels and hyperpolarized by dynamic nuclear polarization with 4.7 % and 3 % polarization, respectively. The longitudinal relaxation constants (T₁) for the labeled acetyl and carboxyl carbonyls were approximately 30 seconds, supporting in vivo imaging and spectroscopy applications. In vitro hydrolysis, transacetylation, and albumin binding of hyperpolarized aspirin were readily monitored in real time by ¹³C‐NMR spectroscopy. Hyperpolarized, double‐labeled aspirin was well tolerated in mice and could be observed by both ¹³C‐MR imaging and ¹³C‐NMR spectroscopy in vivo.     

Exact solutions,conservation laws,bifurcation of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver equation

In the present work, we observe the dynamical behavior of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver (STO) equation. Exact solutions are derived using \({1}/{G^{^{\prime }}}\) expansion and modified Kudryashov methods. The wave transformation is used to transform STO equation into an ordinary differential equation. Combining Runge–Kutta fourth-order and Fourier spectral technique, we use a mixed scheme for the numerical study of STO equation. Since spectral methods expand the solution in trigonometric series resulting into higher-order technique and Runge–Kutta produces improved accuracy, we extract these qualities for a mixed scheme. Results so produced are presented graphically which provide a useful information about the dynamical behavior. Bifurcation behavior of nonlinear and supernonlinear traveling waves of STO equation is studied with the help of bifurcation theory of planar dynamical systems. It is observed that STO equation supports nonlinear solitary wave, periodic wave, shock wave, stable oscillatory wave and most important supernonlinear periodic wave.     

Higher-Order Nonclassical Properties of a Shifted Symmetric Cat State and a One-Dimensional Continuous Superposition of Coherent States

Role of quantum interference in the origin of higher-order nonclassical characteristics of radiation field has been probed vis-à-vis a discrete and a continuous superposition of coherent states. Specifically, the possibilities of observing higher-order nonclassical properties (e.g., higher-order antibunching (HOA), higher-order sub-Poissonian photon statistics (HOSPS), higher-order squeezing (HOS) of Hong-Mandel type and Hillery type) have been investigated using a shifted symmetric cat state that reduces to Yurke-Stoler, even and odd coherent states at various limits. This shifted symmetric cat state which can be viewed as a discrete superposition of coherent states is found to show HOA and HOSPS. Similarly, higher-order nonclassical properties of a one-dimensional continuous superposition of coherent states is also studied here. The investigation has revealed the existence of HOS and HOSPS in the one-dimensional continuous superposition of coherent states studied here. Effect of non-Gaussianity inducing operations (e.g., photon addition and addition followed by subtraction) on these superposition states have also been investigated. Finally, some comparisons have been made between the higher-order nonclassical properties of discrete and continuous superposition of coherent states.