Mixed sums of primes and other terms

In this paper we study mixed sums of primes and linear recurrences. We show that if m=2(mod 4) and m+1 is a prime then $(m^{2^n-1}-1)/(m-1)\not=m^n+p^a$ for any n=3,4,... and prime power p^a. We also prove that if a>1 is an integer, u_0=0, u_1=1 and u_{i+1}=au_i+u_{i-1} for i=1,2,3,..., then all the sums u_m+au_n (m,n=1,2,3,...) are distinct. One of our conjectures states that any integer n>4 can be written as the sum of an odd prime, an odd Fibonacci number and a positive Fibonacci number.Comment: 11 page

Visualization of facet-dependent pseudo-photocatalytic behavior of TiO2 nanorods for water splitting using In situ liquid cell TEM

We report an investigation of the pseudo-photocatalytic behavior of rutile TiO2 nanorods for water splitting observed with liquid cell transmission electron microscopy (TEM). The electron beam serves as a “light” source to initiate the catalytic reaction and a “water-in-salt” aqueous solution is employed as the electrolyte. The observation reveals that bubbles are generated preferentially residing near the {110} facet of a rutile TiO2 nanorod under a low electron dose rate (9.3–18.6 e-/Å2·s). These bubbles are ascribed to hydrogen gas generated from the pseudo-photocatalytic water splitting. As the electron beam current density increases to 93 e-/Å2 ·s, bubbles are also found at the {001} and {111} facets as well as in the bulk liquid solution, demonstrating the dominant effects of water electrolysis by electron beam under higher dose rates. The facet-dependent pseudo-photocatalytic behavior of rutile TiO2 nanorods is further validated using density functional theory (DFT)calculation. Our work establishes a facile liquid cell TEM setup for the study of pseudo-photocatalytic water splitting and it may also be applied to investigation of other photo-activated phenomena occurring at the solid-liquid interfaces

Derivation of 3-D coseismic surface displacement fields for the 2011 Mw 9.0 Tohoku-Oki earthquake from InSAR and GPS measurements

2012-2013 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Sepsis Reduces Bone Strength Before Morphologic Changes Are Identifiable

This is the peer reviewed version of the following article: Puthucheary, Z. A., et al. (2017). "Sepsis Reduces Bone Strength Before Morphologic Changes Are Identifiable." Critical Care Medicine 45(12): e1254-e1261., which has been published in final form at doi: 10.1097/CCM.0000000000002732Supported, in part, by Medicine-Engineering seed grant from National University Health System and Faculty of Engineering at National University Singapore (R-265-000-532-112) (to Drs. Puthucheary, Zeng, and Cove). Singapore National Medical Research Council Transitional Award funding, NMRC/TA/0015/2013 (to Dr. Cove). Ministry of Education (Singapore) Academic Research Grant (R-265-000-495-112) (to Dr. Zeng and Ms. Sun)

Finite element analysis and calculation method of residual flexural capacity of post-fire RC beams

Fire tests and subsequent bending tests of fourreinforced concrete (RC) beamswere performed. Based on these tests, the post-fire performance of RCbeams was further studied using finite element simulation through reasonable selection of suitable thermal and thermodynamic parameters of steel and concrete materials. A thermodynamic model of RC beams with three sides under fire was built using finite element analysis(FEA)software ABAQUS. The FEA model was validated with the results of fire tests. Different factors were taken into account for further parametric studies in fire using the proposed FE model.The results show that the main factors affecting the fire resistance of the beamsare the thickness of the concretecover, reinforcement ratio of longitudinal steel,the fire exposure timeandthe fire exposure sides. Based on the strength reduction formula at high temperature of steel and concrete, animproved section method was proposed to develop a calculation formula to calculate the flexural capacity of RC beams after fire. The theoretical calculation method proposed in this paper shows good agreement with FEA results, which can be used to calculate the flexuralcapacity of RC beams after fire

Toward an understanding of the turbidity measurement of fleterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed

Visualizing size-dependent deformation mechanism transition in Sn

Displacive deformation via dislocation slip and deformation twinning usually plays a dominant role in the plasticity of crystalline solids at room temperature. Here we report in situ quantitative transmission electron microscope deformation tests of single crystal Sn samples. We found that when the sample size was reduced from 450 nm down to 130 nm, diffusional deformation replaces displacive plasticity as the dominant deformation mechanism at room temperature. At the same time, the strength-size relationship changed from “smaller is stronger” to “smaller is much weaker”. The effective surface diffusivity calculated based on our experimental data matches well with that reported in literature for boundary diffusion. The observed change in the deformation mode arises from the sample size-dependent competition between the Hall-Petch-like strengthening of displacive processes and Coble diffusion softening processes. Our findings have important implications for the stability and reliability of nanoscale devices such as metallic nanogaps.National Science Foundation (U.S.) (CMMI-0728069)National Science Foundation (U.S.) (DMR-1008104)National Science Foundation (U.S.) (DMR-1120901)United States. Air Force Office of Scientific Research (FA9550-08-1-0325

The positions of TFIIF and TFIIE in the RNA polymerase II transcription preinitiation complex.

We incorporated the non-natural photoreactive amino acid p-benzoyl-L-phenylalanine (Bpa) into the RNA polymerase II (Pol II) surface surrounding the central cleft formed by the Rpb1 and Rpb2 subunits. Photo-cross-linking of preinitiation complexes (PICs) with these Pol II derivatives and hydroxyl-radical cleavage assays revealed that the TFIIF dimerization domain interacts with the Rpb2 lobe and protrusion domains adjacent to Rpb9, while TFIIE cross-links to the Rpb1 clamp domain on the opposite side of the Pol II central cleft. Mutations in the Rpb2 lobe and protrusion domains alter both Pol II-TFIIF binding and the transcription start site, a phenotype associated with mutations in TFIIF, Rpb9 and TFIIB. Together with previous biochemical and structural studies, these findings illuminate the structural organization of the PIC and the network of protein-protein interactions involved in transcription start site selection