New identities for 7-cores with prescribed BG-rank

Let $\pi$ be a partition. BG-rank$(\pi )$ is defined as an alternating sum of parities of parts of $\pi$ [A. Berkovich, F.G. Garvan, On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo 5 and generalizations, Trans. Amer. Math. Soc. 358 (2006) 703–726. [1]]. Berkovich and Garvan [The BG-rank of a partition and its applications, Adv. in Appl. Math., to appear in $〈$http://arxiv.org/abs/math/0602362$〉$] found theta series representations for the t-core generating functions ${\sum }_{n?0}{a}_{t,j}(n)q^n$, where $a_{t,j}(n)$ denotes the number of t-cores of n with $\text{BG-rank}=j$. In addition, they found positive eta-quotient representations for odd t-core generating functions with extreme values of BG-rank. In this paper we discuss representations of this type for all 7-cores with prescribed BG-rank. We make an essential use of the Ramanujan modular equations of degree seven [B.C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991] to prove a variety of new formulas for the 7-core generating function$\prod _{j?1}\frac{(1-q^{7j}{)}^7}{(1-q^j)}\text{.}$These formulas enable us to establish a number of striking inequalities for $a_{7,j}(n)$ with $j=-1,0,1,2$ and $a_7(n)$, such as$a_7(2n+2)?2a_7(n),a_7(4n+6)?10a_7(n)\text{.}$Here $a_7(n)$ denotes a number of unrestricted 7-cores of n. Our techniques are elementary and require creative imagination only.     

Understanding microscopic binding of human microsomal prostaglandin E synthase-1 with substrates and inhibitors by molecular modeling and dynamics simulation

Microsomal prostaglandin E synthase-1 (mPGES-1) is a promising target for development of next-generation anti-inflammatory drugs. It is crucial for rational design of the next-generation anti-inflammatory drugs to know the three-dimensional (3D) structure of mPGES-1 trimer and to understand how mPGES-1 binds with substrates and inhibitors. In the current work, a 3D structural model of human mPGES-1 trimer has been developed, for the first time, by performing combined homology modeling, molecular docking, and molecular dynamics simulation. The 3D structural model enables us to understand how mPGES-1 binds with its substrates/inhibitors, and the key amino acid residues for the mPGES-1 binding with ligands have been identified. The detailed 3D structures and calculated binding free energies for mPGES-1's binding with substrates and inhibitors are all consistent with available experimental data, suggesting that the 3D model of the mPGES-1 trimer and the enzyme-ligand binding modes are reasonable. The new structural insights obtained from this study should be valuable for rational design of next-generation anti-inflammatory drugs.     

Mechanisms of atomic layer deposition on substrates with ultrahigh aspect ratios

Atomic layer deposition (ALD) appears to be uniquely suited for coating substrates with ultrahigh aspect ratios (> or similar 10(3)), including nanoporous solids. Here, we study the ALD of Cu and Cu3N on the inner surfaces of low-density nanoporous silica aerogel monoliths. Results show that Cu depth profiles in nanoporous monoliths are limited not only by Knudsen diffusion of heavier precursor molecules into the pores, as currently believed, but also by other processes such as the interaction of precursor and reaction product molecules with pore walls. Similar behavior has also been observed for Fe, Ru, and Pt ALD on aerogels. On the basis of these results, we discuss design rules for ALD precursors specifically geared for coating nanoporous solids.     

Optimal state transfer of a single dissipative two-level system

Optimal state transfer of a single two-level system (TLS) coupled to an Ohmic boson bath via off-diagonal TLS-bath coupling is studied by using optimal control theory. In the weak system-bath coupling regime where the time-dependent Bloch-Redfield formalism is applicable, we obtain the Bloch equation to probe the evolution of the dissipative TLS in the presence of a time-dependent external control field. By using the automatic differentiation technique to compute the gradient for the cost functional, we calculate the optimal transfer integral profile that can achieve an ideal transfer within a dimer system in the Fenna-Matthews-Olson (FMO) model. The robustness of the control profile against temperature variation is also analyzed.     

Modern pathology: protein mis-folding and mis-processing in complex disease

Electrostatic and electrochemical properties of bio-molecules, such as proteins, are governed by energy parameters that are, in part dependent on its folding. Disruption of this process can lead to the development of complex, multisystem diseases whose presentation may be organ-dependent. Examples include cystic fibrosis, alpha-1 antitrypsin deficiency, and Alzheimer disease. In addition to explaining exotic pathologic syndromes, an understanding of protein folding mechanisms may facilitate the understanding of less complex diseases and allow the development of novel therapeutic approaches.     

Three-dimensional nanofabrication with elastomeric phase masks

This Feature Article reviews recent work on an optical technique for fabricating, in a single exposure step, three-dimensional (3D) nanostructures with diverse structural layouts. The approach, which we refer to as proximity field nanopatterning, uses conformable, elastomeric phase masks to pattern thick layers of transparent, photosensitive materials in a conformal contact mode geometry. Aspects of the optics, the materials, and the physical chemistry associated with this method are outlined. A range of 3D structures illustrate its capabilities, and several application examples demonstrate possible areas of use in technologies ranging from microfluidics to photonic materials to density gradient structures for chemical release and high-energy density science.     

Hydrogenated carbon clusters produced by highly charged ion impact on solid

The emission of small (hydrogenated) carbon cluster ions C_nHm ⁺ (n =2-22) upon highly charged Xe^q+ (q =20-44) impact on C₈₄ surfaces is studied by means of time-of-flight secondary ion mass spectrometry. The respective stage of hydrogenation/protonation of a certain carbon cluster ion Cn ⁺ is a strong indication for its geometrical structure. From the cluster ion yield as a function of cluster size it can be concluded, that the hydrogenation takes place after the initial carbon cluster formation. The carbon clusters seem to be emitted as an entity in agreement with “equilibrium” and “shock wave” models. Received 4 February 2000     

Strong electromagnetic field localization near the surface of hemicylindrical particles

We theoretically study the forward and backward plane wave illuminations of hemicylindrical dielectric particles with different radii and refractive indices. Near field effects providing strong field enhancement and narrow beam width are obtained from hemicylindrical particles, which can be associated with whispering gallery modes (WGMs) and photonic nano-jets (PNJs). It should be noted that existence of PNJ and WGM effects depending on forward/backward light illuminations is studied for the first time in all-dielectric hemicylindrical particles. Compared to dielectric cylinders, hemicylindrical aided PNJs show relatively small influences of WGM regime, when exists, to PNJ behavior. Under the backward excitation, on the other hand, typical nano-jet is produced. The designed hemicylindrical structure could be implemented in high-resolution optical imaging and sensing applications.     

The Nephroprotective Effect of Zizyphus lotus L. (Desf.) Fruits in a Gentamicin-Induced Acute Kidney Injury Model in Rats: A Biochemical and Histopathological Investigation

Zizyphus lotus L. (Desf.) (Z. lotus) is a medicinal plant largely distributed all over the Mediterranean basin and is traditionally used by Moroccan people to treat many illnesses, including kidney failure. The nephrotoxicity of gentamicin (GM) has been well documented in humans and animals, although the preventive strategies against it remain to be studied. In this investigation, we explore whether the extract of Zizyphus lotus L. (Desf.) Fruit (ZLF) exhibits a protective effect against renal damage produced by GM. Indeed, twenty-four Wistar rats were separated into four equal groups of six each (♂/♀ = 1). The control group was treated orally with distilled water (10 mL/kg); the GM treated group received distilled water (10 mL/kg) and an intraperitoneal injection of GM (80 mg/kg) 3 h after; and the treated groups received ZLF extract orally at the doses 200 or 400 mg/kg and injected intraperitoneally with the GM. All treatments were given daily for 14 days. At the end of the experiment, the biochemical parameters and the histological observation related the kidney function was explored. ZLF treatment has significantly attenuated the nephrotoxicity induced by the GM. This effect was indicated by its capacity to decrease significantly the serum creatinine, uric acid, urea, alkaline phosphatase, gamma-glutamyl-transpeptidase, albumin, calcium, sodium amounts, water intake, urinary volume, and relative kidney weight. In addition, this effect was also shown by the increase in the creatinine clearance, urinary creatinine, uric acid, and urea levels, weight gain, compared to the rats treated only with the GM. The hemostasis of oxidants/antioxidants has been significantly improved with the treatment of ZLF extract, which was shown by a significant reduction in malondialdehydes levels. Histopathological analysis of renal tissue was correlated with biochemical observation. Chemical analysis by HPLC-DAD showed that the aqueous extract of ZLF is rich in phenolic compounds such as 3-hydroxycinnamic acid, catechin, ferulic acid, gallic acid, hydroxytyrosol, naringenin, p- coumaric Acid, quercetin, rutin, and vanillic acid. In conclusion, ZLF extract improved the nephrotoxicity induced by GM, through the improvement of the biochemical and histological parameters and thus validates its ethnomedicinal use.     

Dynamical Localization for Unitary Anderson Models

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.