Phi Function Research Articles

Polarization Studies of Resonant Forbidden Reflections in Liquid Crystals

We report the results of resonant x-ray diffraction experiments performed on thick films of a biaxial liquid crystal made of achiral bent-core molecules. Polarization properties of forbidden reflections are observed as a function of the sample rotation angle phi about the scattering vector Q for the first time on a fluid material. The experimental data are successfully analyzed within a tensor structure factor model by taking the nonperfect alignment of the liquid crystal into account. The local structure of the B2 mesophase is hence determined to be SmC_{S}P_{A}.

Sum Frequency Generation Spectroscopy of Dicyanamide Based Room-Temperature Ionic Liquids. Orientation of the Cation and the Anion at the Gas−liquid Interface

The orientation of the cation and the anion of room-temperature ionic liquids using sum frequency generation vibrational spectroscopy is reported. The ionic liquids are based on butyl-methyl imidazolium [BMIM]+ and hexyl-tributyl ammonium [N6444]+ together with dicyanamide [DCA]- as the anion. The tilt angle of the C3 axis of the methyl group from the alkyl chain in the cations was found to vary from 52 degrees to 80 degrees as a function of the distribution width sigma (which ranges from 0 degrees to 30 degrees with respect to the surface normal) for [BMIM][DCA] and similarly for [N6444][DCA]. The orientation of the C2 axis in the dicyanamide anion as a function of the twist angle phi, varied between 46 degrees and 90 degrees for [BMIM][DCA] and from 53 degrees to 90 degrees for [N6444][DCA]. These results suggest the presence of both ionic species at the gas-liquid interface and help describe the behavior of a simple inorganic anion at the surface.

DFT studies of the conformational/structural dependencies of geminal 1H,1H scalar coupling 2J(H,H′) in substituted methanes

A study is presented of the structural dependencies for scalar, interproton J-coupling across two bonds in a series of substituted methanes. The coupled perturbed, density functional theory method with a B3PW91 functional and aug-cc-pVTZ-J basis sets is used to examine coupling between geminal protons (2)J(H,H') in methane and a series of substituted compounds CH(3)X (X = CH3, CH(2)CH(3), CH=CH2, CH=O, and NH2) as functions of the dihedral angle phi measured about the C1-X2 bonds. All four contributions are obtained but all conformational effects are dominated by the Fermi contact term. Simple linear combination of atomic orbitals (LCAO)-molecular orbital (MO) sum-over-states methods are used to examine the relationships of the coupling constants with dihedral angles as well as internal H-C-H and H-C1-X2 angles. This study explores some novel aspects of geminal H-H coupling including an analysis of the asymmetry in the conformational dependencies arising from non-next-nearest neighbor interactions. For each of the substituted methanes, explicit trigonometric/exponential expressions are given and these accurately reproduce the (2)J(H,H') structural dependencies with standard deviations usually less than 0.03 Hz. The molecular structures for representative bicyclic molecules were fully optimized, and DFT results for (2)J(H,H') reproduce all the trends in the experimental data. A discussion is given on the applicability of the equations for H--H coupling in the substituted methanes to coupling in the bicyclic molecules.

Weissenberg Reflection High-Energy Electron Diffraction for Surface Crystallography

The principle of a Weissenberg camera is applied to surface crystallographic analysis by reflection high-energy electron diffraction. By removing inelastic electrons and measuring hundreds of patterns as a function of sample rotation angle phi, kinematical analysis can be performed over a large volume of reciprocal space. The data set is equivalent to a three-dimensional stack of Weissenberg photographs. The method is applied to analysis of an Si(111)-square root of 3 x square root of 3-Ag surface, and the structural data obtained are in excellent agreement with the known atomic structure.

On the Proof of a Theorem of Pálfy

Pálfy proved that a group $G$ is a CI-group if and only if $\vert G\vert = n$ where either $\gcd(n,\varphi(n)) = 1$ or $n = 4$, where $\varphi$ is Euler's phi function. We simplify the proof of "if $\gcd(n,\varphi(n)) = 1$ and $G$ is a group of order $n$, then $G$ is a CI-group".

Arithmetic properties of positive integers with fixed digit sum

In this paper, we look at various arithmetic properties of the set of those positive integers n whose sum of digits in a fixed base b>1 is a fixed positive integers s . For example, we prove that such integers can have many prime factors, that they are not very smooth, and that most such integers have a large prime factor dividing the value of their Euler \phi function.

Domain Requirement for the Membrane Trafficking and Targeting of Syntaxin 1A

Syntaxin plays a key role in intracellular membrane fusion in eukaryotic cells. The function of syntaxin relies on its proper trafficking to and targeting at the target membrane. The mechanisms underlying the trafficking and targeting of syntaxin to its physiological sites remain poorly understood. Here we have analyzed the trafficking of syntaxin 1A in INS-1 and CHO cells. We have identified the transmembrane domain together with several flanking positive-charged amino acids as the minimal domain required for the membrane delivery. Interestingly, we found that SNARE motif-exposed syntaxin 1A mutants were retained in endoplasmic reticulum (ER) and failed to transport to the cell surface in the absence of SNAP-25, suggesting that the exposure of the SNARE motif causes ER retention and complexation with SNAP-25 helps the ER escape. Finally, our data propose two key roles for the H(abc) domain: to protect nonspecific interaction by masking the SNARE motif and to participate in the clustering of syntaxin 1A to the fusion sites in the plasma membrane.

Values of the Euler phi function not divisible by a given odd prime

An asymptotic formula is given for the number of integers n≤x for which φ(n) is not divisible by a given odd prime.

Ab initiostudy of alanine polypeptide chain twisting

We have investigated the potential energy surfaces for alanine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles and , which are widely used for the characterization of the polypeptide chains. These particular degrees of freedom are essential for the characterization of the proteins folding process. Calculations have been carried out within the ab initio theoretical framework based on the density functional theory and accounting for all the electrons in the system. We have determined stable conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods and with the available experimental data extracted from the Protein Data Base. This comparison demonstrates a reasonable correspondence of the most prominent minima on the calculated potential energy surfaces to the experimentally measured angles and for alanine chains appearing in native proteins. We have also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.

The Physiological Role of the Ribulose Monophosphate Pathway in Bacteria and Archaea

3-Hexulose-6-phosphate synthase (HPS) and 6-phospho-3-hexuloisomerase (PHI) are the key enzymes of the ribulose monophosphate pathway. This pathway, which was originally found in methylotrophic bacteria, is now recognized as a widespread prokaryotic pathway involved in formaldehyde fixation and detoxification. Recent progress, involving biochemical and genetic approaches in elucidating the physiological functions of HPS and PHI in methylotrophic as well as non-methylotrophic bacteria are described in this review. HPS and PHI orthologs are also found in a variety of archaeal strains. Some archaeal HPS orthologs are fused with other genes to form single ORF (e.g., the hps-phi gene of Pyrococcus spp. and the faeB-hpsB gene of Methanosarcina spp). These fused gene products exhibit functions corresponding to the individual enzyme activities, and are more efficient than equivalent systems made up of discrete enzymes. Recently, a novel metabolic function for HPS and PHI has been proposed in which these enzymes catalyze the reverse reaction for the biosynthesis of pentose phosphate in some archaeal strains. Thus the enzyme system plays a different role in bacteria and archaea by catalyzing the forward and reverse reactions respectively.

Effect of fabrication errors on superresolution property of a pupil filter

Three analytical models have been established for superresolution parameters G(Ae), G(Te), and S(e) related to transmission function A(rho), phase function of phi(rho), and the structural parameters with fabrication errors of an N-zone circular-symmetrical superresolution pupil filter. These new models established, directly relate the superresolution parameters of an N-zone super-resolution pupil filter to its fabrication errors to make the quantitative analyses of the effect of fabrication errors easier, thereby providing a theoretical basis for the analysis, design, and fabrication of an N-zone super-resolution pupil filter. The models established for G(Ae), G(Te), and S(e) have been used to analyze the effect of the fabrication errors of a three-zone phase-only pupil filter on its superresolution property, to verify their validities.

Recurrence Relations for the Lerch Φ-Function and Applications

In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those obtained by H. M. Srivastava, M. L. Glasser and V. Adamchik [Z. Anal. Anwendungen 19 (2000), 831 – 846] are pointed out, emphasizing the usefulness of this approach with some meaningful examples.

An 802.11g WLAN SoC

A single-chip IEEE-802.11g-compliant wireless LAN system-on-a-chip (SoC) that implements all RF, analog, digital PHY and MAC functions has been integrated in a 0.18-/spl mu/m CMOS technology. The IC transmits 0-dBm EVM-compliant output power for a 64-QAM OFDM signal. The overall receiver sensitivities are better than -92 and -73 dBm for data rates of 6 and 54Mb/s, respectively.

Velocity distributions in dilute granular systems

We investigate the idea that velocity distributions in granular gases are determined mainly by eta, the coefficient of restitution and q, which measures the relative importance of heating (or energy input) to collisions. To this end, we study by numerical simulation the properties of inelastic gases as functions of eta, concentration phi, and particle number N with various heating mechanisms. For a wide range of parameters, we find Gaussian velocity distributions for uniform heating and non-Gaussian velocity distributions for boundary heating. Comparison between these results and velocity distributions obtained by other heating mechanisms and for a simple model of a granular gas without spatial degrees of freedom, shows that uniform and boundary heating can be understood as different limits of q, with q>>1 and q < or approximately 1 respectively. We review the literature for evidence of the role of q in the recent experiments.

Measurements of bottom-antibottom azimuthal production correlations in proton-antiproton collisions ats=1.8 TeV

We have measured the azimuthal angular correlation of bottom anti-bottom production, using 86.5 pb-1 of data collected by Collider Detector at Fermilab (CDF) in proton anti-proton collisions at sqrt{s}=1.8 TeV during 1994-1995. In high-energy p-pbar collisions, such as at the Tevatron, bottom anti-bottom production can be schematically categorized into three mechanisms. The leading-order (LO) process is ``flavor creation,'' where both the bottom and anti-bottom quarks substantially participate in the hard scattering and result in a distinct back-to-back signal in final state. The ``flavor excitation'' and the ``gluon splitting'' processes, which appear at next-leading-order (NLO), are known to make a comparable contribution to total bottom anti-bottom cross section, while providing very different opening angle distributions from the LO process. An azimuthal opening angle between bottom and anti-bottom, Delta phi, has been used for the correlation measurement to probe the interaction creating bottom anti-bottom pairs. The Delta phi distribution has been obtained from two different methods. One method measures the Delta phi between bottom hadrons using events with two reconstructed secondary vertex tags. The other method uses b-bbar --> (J/psi X)(l X') events, where the charged lepton (l) is an electron or a muon, to measure Delta phi between bottom quarks. The bottom anti-bottom purity is determined as a function of Delta phi by fitting the decay length of the J/psi and the impact parameter of the lepton. Both methods quantify the contribution from higher-order production mechanisms by the fraction of the b-bbar pairs produced in the same azimuthal hemisphere, f_toward. The measured f_toward values are consistent with both parton shower Monte Carlo and NLO QCD predictions.

Telescoping, rational-valued series, and zeta functions

We give an effective procedure for determining whether or not a series ∑ n = M N r ( n ) \sum _{n=M}^{N}r\left ( n\right ) telescopes when r ( n ) r\left ( n\right ) is a rational function with complex coefficients. We give new examples of series ( ∗ ) ∑ n = 1 ∞ r ( n ) \left ( \ast \right ) \sum _{n=1}^{\infty }r\left ( n\right ) , where r ( n ) r\left ( n\right ) is a rational function with integer coefficients, that add up to a rational number. Generalizations of the Euler phi function and the Riemann zeta function are involved. We give an effective procedure for determining which numbers of the form ( ∗ ) \left ( \ast \right ) are rational. This procedure is conditional on 3 conjectures, which are shown to be equivalent to conjectures involving the linear independence over the rationals of certain sets of real numbers. For example, one of the conjectures is shown to be equivalent to the well-known conjecture that the set { ζ ( s ) : s = 2 , 3 , 4 , … } \left \{ \zeta \left ( s\right ) :s=2,3,4,\dots \right \} is linearly independent, where ζ ( s ) = ∑ n − s \zeta \left ( s\right ) =\sum n^{-s} is the Riemann zeta function. Some series of the form ∑ n s ( n r , n + 1 r , ⋯ , n + k r ) \sum _{n}s\left ( \sqrt [r]{n},\sqrt [r]{n+1} ,\cdots ,\sqrt [r]{n+k}\right ) , where s s is a quotient of symmetric polynomials, are shown to be telescoping, as is ∑ 1 / ( n ! + ( n − 1 ) ! ) \sum 1/(n!+\left ( n-1\right ) !) . Quantum versions of these examples are also given.

Two-particle irreducible finite temperature effective potential of theO(N)linear sigma model in1+1dimensions at next-to-leading order of1/N

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.

Chromatic adaptation, perceived location, and color tuning properties

We have studied the influence of chromatic adaptation upon the perceived visual position of a test stimulus using a Vernier alignment task. Maximum and minimum offsets in spatial position are generated when the adapting and test stimuli lie on the same and orthogonal axes in MBDKL color space, respectively. When the test stimuli lie on intermediate color axes, the measured positional shifts decrease as a function of the angular separation in color space (phi) from the adapting stimulus. At low stimulus contrasts, these shifts follow a sinusoidal function of phi and exhibit broad chromatic tuning and can be accounted for by a model in which the centroid is extracted from the linear combination of after-image, formed by the adapting stimulus, and the test stimulus. Such linear, broadband behavior is consistent with the response properties of chromatic neurons in the precortical visual pathway. At high contrast, and when adaptation gets closer to the S/(L+M) axis, the tuning functions become narrower and require sinusoids raised to increasingly higher exponents in order to describe the data. This narrowing of chromatic tuning is consistent with the tuning properties of chromatic neurons in the striate cortex, and implies the operation of a nonlinear mechanism in the combination of cone outputs.

Tryptophan chemical shift in peptides and proteins: a solid state carbon-13 nuclear magnetic resonance spectroscopic and quantum chemical investigation.

We have obtained the carbon-13 nuclear magnetic resonance spectra of a series of tryptophan-containing peptides and model systems, together with their X-ray crystallographic structures, and used quantum chemical methods to predict the (13)C NMR shifts (or shieldings) of all nonprotonated aromatic carbons (C(gamma), C(delta 2) and C(epsilon 2). Overall, there is generally good accord between theory and experiment. The chemical shifts of Trp C(gamma) in several proteins, hen egg white lysozyme, horse myoglobin, horse heart cytochrome c, and four carbonmonoxyhemoglobins, are also well predicted. The overall Trp C(gamma) shift range seen in the peptides and proteins is 11.4 ppm, and individual shifts (or shieldings) are predicted with an rms error of approximately 1.4 ppm (R value = 0.86). Unlike C(alpha) and N(H) chemical shifts, which are primarily a function of the backbone phi,psi torsion angles, the Trp C(gamma) shifts are shown to be correlated with the side-chain torsion angles chi(1) and chi(2) and appear to arise, at least in part, from gamma-gauche interactions with the backbone C' and N(H) atoms. This work helps solve the problem of the chemical shift nonequivalences of nonprotonated aromatic carbons in proteins first identified over 30 years ago and opens up the possibility of using aromatic carbon chemical shift information in structure determination.

The Decamethylferrocene(+/0) Electrode Reaction in Organic Solvents at Variable Pressure and Temperature

Half-wave potentials E(1/2) relative to a Ag/Ag(+) electrode, mean diffusion coefficients D, and standard electrode reaction rate constants k(el) are reported for the decamethylferrocene(+/0) couple (DmFc(+/0)) in nine organic solvents at variable pressure and (for five solvents) temperature. Limited data on the ferrocene(+/0) (Fc(+/0)) and Fe(phen)(3)(3+/2+) electrode reactions are included for comparison. Although E(1/2) for DmFc(+/0) correlates only loosely with the reciprocal of the solvent dielectric constant epsilon at ambient pressure, its pressure dependence expressed as the volume of reaction Delta V(cell) is a linear function of Phi = (1/epsilon)( partial differential ln epsilon/ partial differential P)(T) (the Drude-Nernst relation). Interpretation of the temperature dependence data is made difficult by enthalpy-entropy compensation. Measurements of D for solutions containing 0.5 mol L(-1) tetrabutylammonium perchlorate (TBAP) at 25 degrees C and ambient pressure are inversely proportional to the viscosities eta of the pure solvents as expected from the Stokes-Einstein relation, despite the fact that increasing [TBAP] results in increased eta. The activation volume Delta V(diff)(++) for diffusion of DmFc(+/0) ranges from 7 to 17 cm(3) mol(-1) and generally increases with increasing eta and thus with increasing [TBAP]. The activation volumes Delta V(el)(++) for the electrode reactions of DmFc(+/0) and Fc(+/0) are all positive, equaling the corresponding Delta V(diff)(++) values within the experimental uncertainty and contrast sharply with the negative Delta V(ex)(++) values characteristic of the corresponding self-exchange reactions in homogeneous solution. These facts, together with the thermal activation parameters, point to solvent dynamical control of the electrode (but not the homogeneous self-exchange) reactions. The apparent radii of the electroactive species according to the Drude-Nernst and Stokes-Einstein relations cannot be satisfactorily related to their crystallographic radii and are better regarded as adjustable parameters with limited physical significance.