Time-like solutions to the Lorentz force equation in time-dependent electromagnetic and gravitational fields

We find existence and multiplicity results for time-like spatially periodic trajectories of massive particles carrying an electric charge q and subjected to time-dependent gravitational and electromagnetic fields. Such trajectories are obtained by projecting, on the base space-time, time-like geodesics with respect to a suitable Kaluza-Klein metric.     

On actually computable bijections between ℕ and Q +

We present three different ways of getting an actually computable enumeration of Q ⁺ in the sense of being able to know exactly which rational occupies a given position and vice versa. The first enumeration is based on the Pierce expansion model for representing real numbers. The other two are based on regular continued fractions.The first and third authors were supported by UPF Grant, Support d'Iniciació a la Recerca, # F3087613.     

组织蛋白酶B响应的超极化129Xe MRI探针对肺癌细胞的超灵敏探测

组织蛋白酶B（Cat B）是一种溶酶体半胱氨酸蛋白酶,在细胞代谢中起重要作用.已有研究表明Cat B在肺癌细胞中会过表达.因此,细胞内Cat B水平的检测非常重要.迄今为止,细胞内Cat B的检测方法主要为荧光成像,但该技术受限于渗透性和自发荧光背景干扰.为了解决这些问题,我们设计了一种基于超极化¹²⁹Xe磁共振成像的新型探针.它由一个作为¹²⁹Xe核磁共振（NMR）报告基团的穴番分子笼和一个作为Cat B特异性可裂解基团的酰胺键组成.当探针与Cat B相互作用时,酰胺键的断裂会导致其¹²⁹Xe化学位移发生变化.结合超极化-化学交换饱和转移（Hyper-CEST）技术,可为Cat B提供一种新颖的检测方法.     

Exact solutions of nonlinear time fractional partial differential equations by sub‐equation method

In this article, the sub‐equation method is presented for finding the exact solutions of a nonlinear fractional partial differential equations. For this, the fractional complex transformation method has been used to convert fractional‐order partial differential equation to ordinary differential equation. The fractional derivatives are described in Jumarie's the modified Riemann–Liouville sense. We apply to this method for the nonlinear time fractional differential equations. With the aid of symbolic computation, a variety of exact solutions for them are obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Casimir effect in the Hořava–Lifshitz gravity with a cosmological constant

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M$M$ and radius R$R$. To this end, we take into account a static and spherically symmetric solution of Ho?ava–Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant.     

Analytic solutions in the dyon black hole with a cosmic string: Scalar fields,Hawking radiation and energy flux

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux.     

Biomembrane Interactions of Functionalized Cryptophane‐A: Combined Fluorescence and 129Xe NMR Studies of a Bimodal Contrast Agent

Fluorescent derivatives of the ¹²⁹Xe NMR contrast agent cryptophane‐A were obtained by functionalization with near infrared fluorescent dyes DY680 and DY682. The resulting conjugates were spectrally characterized, and their interaction with giant and large unilamellar vesicles of varying phospholipid composition was analyzed by fluorescence and NMR spectroscopy. In the latter, a chemical exchange saturation transfer with hyperpolarized ¹²⁹Xe (Hyper‐CEST) was used to obtain sufficient sensitivity. To determine the partitioning coefficients, we developed a method based on fluorescence resonance energy transfer from Nile Red to the membrane‐bound conjugates. This indicated that not only the hydrophobicity of the conjugates, but also the phospholipid composition, largely determines the membrane incorporation. Thereby, partitioning into the liquid‐crystalline phase of 1,2‐dipalmitoyl‐sn‐glycero‐3‐phosphocholine was most efficient. Fluorescence depth quenching and flip‐flop assays suggest a perpendicular orientation of the conjugates to the membrane surface with negligible transversal diffusion, and that the fluorescent dyes reside in the interfacial area. The results serve as a basis to differentiate biomembranes by analyzing the Hyper‐CEST signatures that are related to membrane fluidity, and pave the way for dissecting different contributions to the Hyper‐CEST signal.     

“Direct” 13C Hyperpolarization of 13C‐Acetate by MicroTesla NMR Signal Amplification by Reversible Exchange (SABRE)

Herein, we demonstrate “direct” ¹³C hyperpolarization of ¹³C‐acetate via signal amplification by reversible exchange (SABRE). The standard SABRE homogeneous catalyst [Ir‐IMes; [IrCl(COD)(IMes)], (IMes=1,3‐bis(2,4,6‐trimethylphenyl), imidazole‐2‐ylidene; COD=cyclooctadiene)] was first activated in the presence of an auxiliary substrate (pyridine) in alcohol. Following addition of sodium 1‐¹³C‐acetate, parahydrogen bubbling within a microtesla magnetic field (i.e. under conditions of SABRE in shield enables alignment transfer to heteronuclei, SABRE‐SHEATH) resulted in positive enhancements of up to ≈100‐fold in the ¹³C NMR signal compared to thermal equilibrium at 9.4 T. The present results are consistent with a mechanism of “direct” transfer of spin order from parahydrogen to ¹³C spins of acetate weakly bound to the catalyst, under conditions of fast exchange with respect to the ¹³C acetate resonance, but we find that relaxation dynamics at microtesla fields alter the optimal matching from the traditional SABRE‐SHEATH picture. Further development of this approach could lead to new ways to rapidly, cheaply, and simply hyperpolarize a broad range of substrates (e.g. metabolites with carboxyl groups) for various applications, including biomedical NMR and MRI of cellular and in vivo metabolism.     

Parahydrogen‐Induced Hyperpolarization of Gases

Imaging of gases is a major challenge for any modality including MRI. NMR and MRI signals are directly proportional to the nuclear spin density and the degree of alignment of nuclear spins with applied static magnetic field, which is called nuclear spin polarization. The level of nuclear spin polarization is typically very low, i.e., one hundred thousandth of the potential maximum at 1.5 T and a physiologically relevant temperature. As a result, MRI typically focusses on imaging highly concentrated tissue water. Hyperpolarization methods transiently increase nuclear spin polarizations up to unity, yielding corresponding gains in MRI signal level of several orders of magnitude that enable the 3D imaging of dilute biomolecules including gases. Parahydrogen‐induced polarization is a fast, highly scalable, and low‐cost hyperpolarization technique. The focus of this Minireview is to highlight selected advances in the field of parahydrogen‐induced polarization for the production of hyperpolarized compounds, which can be potentially employed as inhalable contrast agents.