Values Of Zeta Research Articles

Classical Values of Zeta, as Simple as Possible But Not Simpler

Classical Values of Zeta, as Simple as Possible But Not Simpler

Detecting 𝛽 elements in iterated algebraic K-theory

The Lichtenbaum–Quillen conjecture (LQC) relates special values of zeta functions to algebraic K-theory groups. The Ausoni–Rognes red-shift conjectures generalize the LQC to higher chromatic heights in a precise sense. In this paper, we propose an alternate generalization of the LQC to higher chromatic heights and give evidence for it at height two. In particular, if the n n -th Greek letter family is detected by a commutative ring spectrum R R , then we conjecture that the n + 1 n+1 -st Greek letter family will be detected by the algebraic K-theory of R R . We prove this in the case n = 1 n=1 for R = K ( F q ) R=\mathrm {K}(\mathbb {F}_q) modulo ( p , v 1 ) (p,v_1) where p ≥ 5 p\ge 5 and q = ℓ k q=\ell ^k is a prime power generator of the units in Z / p 2 Z \mathbb {Z}/p^2\mathbb {Z} . In particular, we prove that the commutative ring spectrum K ( K ( F q ) ) \mathrm {K}(\mathrm {K}(\mathbb {F}_q)) detects the part of the p p -primary β \beta -family that survives mod ( p , v 1 ) (p,v_1) . The method of proof also implies that these β \beta elements are detected in iterated algebraic K-theory of the integers. Consequently, one may relate iterated algebraic K-theory groups of the integers to integral modular forms satisfying certain congruences.

ON THE PARITY RESULT FOR MULTIPLE DIRICHLET SERIES

In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, such as the Mordell-Tornheim type of multiple zeta values, zeta values of the root systems and so on. Moreover, we can give an explicit expression in terms of lower series by using the main theorem.

Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines

For an arbitrary complex number ane 0 we consider the distribution of values of the Riemann zeta-function zeta at the a-points of the function Delta which appears in the functional equation zeta (s)=Delta (s)zeta (1-s). These a-points delta _a are clustered around the critical line 1/2+imathbb {R} which happens to be a Julia line for the essential singularity of zeta at infinity. We observe a remarkable average behaviour for the sequence of values zeta (delta _a).

Enhancing flashover strength along oil/pressboard interface using nanofluids

One of the weakest paths for electrical discharge in power transformers is oil/pressboard interface. So, in this study it is aimed to enhance the flashover resistance of such interface through using the concept of nanofluids. Nanofluid impregnated pressboard were prepared using two different types of nanoparticles. These types are Alumina (Al2O3) and Titania (TiO2) which have different values of zeta (ζ) potential that had been experimentally measured. Flashover tests are carried out at pressboard interface with nanofluids and mineral oil. Three conditions of oil flow are considered, static and turbulent dynamic flow with two different circulating velocities. Flashover strength of nanofluid impregnated pressboard was tested for different weight fractions of nanoparticles and was compared to that of the base mineral oil. In each test, the value and polarity of applied AC voltage at the instant of flashover was recorded. Weibull distribution was used for analyzing flashover strength data. The polarity at which flashover occurred was positive in all tests. Physical mechanisms have been discussed considering electron trapping and double layer model of nanoparticles.

Rheological properties and structural features of coconut milk emulsions stabilized with maize kernels and starch

In this study, maize kernels and starch with different amylose contents at the same concentration were added to coconut milk. The nonionic composite surfactants were used to prepare various types of coconut milk beverages with optimal stability, and their fluid properties were studied. The steady and dynamic rheological property tests show that the loss modulus (G″) of coconut milk is larger than the storage modulus (G′), which is suitable for the pseudoplastic fluid model and has a shear thinning effect. As the droplet size of the coconut milk fluid changed by the addition of maize kernels and starch, the color intensity, ζ-potential, interfacial tension and stability of the sample significantly improved. The addition of the maize kernels significantly reduced the size of the droplets (p < 0.05). The potential values of zeta (ζ) and the surface tension of the coconut milk increased. Based on the differential scanning calorimetry (DSC) measurement, the addition of maize kernels leads to an increase in the transition temperature, especially in samples with a high amylose content. The higher transition temperature can be attributed to the formation of some starches and lipids and the partial denaturation of proteins in coconut milk, but phase separation occurs. These results may be helpful for determining the properties of maize kernels in food-containing emulsions (such as sauces, condiments, and beverages) that achieve the goal of physical stability.

Universal dimensional crossover of domain wall dynamics in ferromagnetic films

The magnetic domain wall motion driven by a magnetic field is studied in (Ga,Mn)As and (Ga,Mn)(As,P) films of different thicknesses. In the thermally activated creep regime, a kink in the velocity curves and a jump of the roughness exponent evidence a dimensional crossover in the domain wall dynamics. The measured values of the roughness exponent zeta_{1d} = 0.62 +/- 0.02 and zeta_{2d} = 0.45 +/- 0.04 are compatible with theoretical predictions for the motion of elastic line (d = 1) and surface (d = 2) in two and three dimensional media, respectively.

Viscous cosmology in new holographic dark energy model and the cosmic acceleration

In this work, we study a flat Friedmann–Robertson–Walker universe filled with dark matter and viscous new holographic dark energy. We present four possible solutions of the model depending on the choice of the viscous term. We obtain the evolution of the cosmological quantities such as scale factor, deceleration parameter and transition redshift to observe the effect of viscosity in the evolution. We also emphasis upon the two independent geometrical diagnostics for our model, namely the statefinder and the Om diagnostics. In the first case we study new holographic dark energy model without viscous and obtain power-law expansion of the universe which gives constant deceleration parameter and statefinder parameters. In the limit of the parameter, the model approaches to Lambda CDM model. In new holographic dark energy model with viscous, the bulk viscous coefficient is assumed as zeta =zeta _{0}+zeta _{1}H, where zeta _{0} and zeta _{1} are constants, and H is the Hubble parameter. In this model, we obtain all possible solutions with viscous term and analyze the expansion history of the universe. We draw the evolution graphs of the scale factor and deceleration parameter. It is observed that the universe transits from deceleration to acceleration for small values of zeta in late time. However, it accelerates very fast from the beginning for large values of zeta . By illustrating the evolutionary trajectories in r-s and r-q planes, we find that our model behaves as an quintessence like for small values of viscous coefficient and a Chaplygin gas like for large values of bulk viscous coefficient at early stage. However, model has close resemblance to that of the Lambda CDM cosmology in late time. The Om has positive and negative curvatures for phantom and quintessence models, respectively depending on zeta . Our study shows that the bulk viscosity plays very important role in the expansion history of the universe.

Preparation, characterization, drug release and computational modelling studies of antibiotics loaded amorphous chitin nanoparticles

We present a computational investigation of binding affinity of different types of drugs with chitin nanocarriers. Understanding the chitn polymer-drug interaction is important to design and optimize the chitin based drug delivery systems. The binding affinity of three different types of anti-bacterial drugs Ethionamide (ETA) Methacycline (MET) and Rifampicin (RIF) with amorphous chitin nanoparticles (AC-NPs) were studied by integrating computational and experimental techniques. The binding energies (BE) of hydrophobic ETA, hydrophilic MET and hydrophobic RIF were −7.3kcal/mol, −5.1kcal/mol and −8.1kcal/mol respectively, with respect to AC-NPs, using molecular docking studies. This theoretical result was in good correlation with the experimental studies of AC-drug loading and drug entrapment efficiencies of MET (3.5±0.1 and 25± 2%), ETA (5.6±0.02 and 45±4%) and RIF (8.9±0.20 and 53±5%) drugs respectively. Stability studies of the drug encapsulated nanoparticles showed stable values of size, zeta and polydispersity index at 6°C temperature. The correlation between computational BE and experimental drug entrapment efficiencies of RIF, ETA and MET drugs with four AC-NPs strands were 0.999 respectively, while that of the drug loading efficiencies were 0.854 respectively. Further, the molecular docking results predict the atomic level details derived from the electrostatic, hydrogen bonding and hydrophobic interactions of the drug and nanoparticle for its encapsulation and loading in the chitin-based host-guest nanosystems. The present results thus revealed the drug loading and drug delivery insights and has the potential of reducing the time and cost of processing new antibiotic drug delivery nanosystem optimization, development and discovery.

The critical role of didodecyldimethylammonium bromide on physico-chemical, technological and biological properties of NLC

Exploiting the experimental factorial design and the potentiality of Turbiscan AG Station, we developed and characterized unmodified and DDAB-coated NLC prepared by a low energy organic solvent free phase inversion temperature technique. A 22 full factorial experimental design was developed in order to study the effects of two independent variables (DDAB and ferulic acid) and their interaction on mean particle size and zeta potential values. The factorial planning was validated by ANOVA analysis; the correspondence between the predicted values of size and zeta and those measured experimentally confirmed the validity of the design and the equation applied for its resolution. The DDAB-coated NLC were significantly affected in their physico-chemical properties by the presence of DDAB, as showed by the results of the experimental design. The coated NLC showed higher physical stability with no particles aggregation compared to the unmodified NLC, as demonstrated by Turbiscan® AGS measurements. X-ray diffraction, Raman spectroscopy and Cryo-TEM images allowed us to assert that DDAB plays a critical role in increasing the lipids structural order with a consequent enhancement of the NLC physical stability. Furthermore, the results of the in vitro biological studies allow the revisiting of the role of DDAB to the benefit of glioblastoma treatment, due to its efficacy in increasing the NLC uptake and reducing the viability of human glioblastoma cancer cells (U87MG).

Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of \(\mathrm{SL }_2(\mathbb {C})\) to the corresponding Reidemeister torsion. While the analytic torsion is a spectral invariant of the manifold, the Reidemeister torsion is of combinatorial nature. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.

Effect of Discrete Macroion Charge Distributions on Electric Double Layer of a Spherical Macroion

The effect of replacing the conventional uniform macroion surface charge density with discrete macroion charge distributions on the structure of electric double layer (EDL) of a spherical macroion has been investigated by Monte Carlo (MC) simulations. Two discrete models have been investigated in addition to the central macroion charge: point charges localized on the macroion surface and finite-sized charges protruding into the solution. Both models have been studied with fixed and mobile macroion charges. The radial functions of local densities and electrostatic potential in EDL, are calculated and compared to the results obtained for the central macroion charge distribution. It is concluded that the model of charge distribution significantly affects the EDL structure close to the macroion, while the effect is much weaker at larger distances. With point charges localized on the macroion surface, counterions become stronger accumulated to the macroion, as a result the absolute values of surface potential ϕ0 and zeta ξ potential are decreased. With protruding charges, the excluded volume effect dominates over the increased correlation ability; hence the counterions are less accumulated near the macroions and the absolute values of ϕ0 and ξ potentials are increased.

On the Coates-Sinnott conjecture for CM fields

Let k be a totally real number field and F be a totally real or CM field (a quadratic extension of a totally real field) that is a finite abelian extension over k. Let FΣ be the maximal algebraic extension of F unramified outside the Archimedean primes and all primes above p, and let GΣ(F)=Gal(FΣ/F). The cohomological Coates–Sinnott conjecture for an odd prime number p asserts that a certain element constructed by the special values of the partial zeta functions annihilates the Galois cohomology group H2(GΣ (F), ℤp(n+1)), where n is a positive integer. If we assume that the Quillen–Lichtenbaum conjecture holds, then the Galois cohomology group is isomorphic to the p-part of the K-group K2n(풪F), where 풪F is the ring of the algebraic integers of F. Popescu proved the cohomological Coates–Sinnott conjecture for totally real fields F and odd prime numbers p satisfying p ∤ [F:F∩k∞], where k∞ is the cyclotomic ℤp-extension of k. In this paper, we will give a simple proof of the conjecture for a totally real or CM field F and odd prime numbers p satisfying p ∤ [F:F∩k∞].

Preparation and optimization of PIT solid lipid nanoparticles via statistical factorial design

The objective of this study was the preparation, physico-chemical characterization and statistical optimization of cationic solid lipid nanoparticles (SLN) prepared by the PIT method as potential carrier for gene therapy, emphasizing the application of factorial design in such a kind of studies. The preliminary screening from a physico-chemical point of view on three cationic lipids (CTAB, DDAB and DOTAP), selected on the basis of their different chemical structure and increasing lipophilicity, allowed us to select SLN with DOTAP, due to its higher zeta potential and smaller particle size. Afterward, a 22 full factorial experimental design was developed in order to study the effects of two independent variables (amount of DOTAP and concentration of lipid matrix) and their interaction on mean particle size and zeta potential values. The factorial planning was validated by ANOVA analysis; the correspondence between the predicted values of size and zeta and those measured experimentally confirmed the validity of the design and the equation applied for its resolution. The factorial design showed a significant influence of the independent variables on the selected parameters; in particular, a higher effect of DOTAP was observed on zeta potential value. Different dilutions of the optimized SLN containing 7% w/w of cutina CP and 1% w/w of DOTAP, with size and zeta potential values respectively of 462.9 nm and 50.8 mV, were in vitro examined to evaluate the possible cytotoxicity on two models of cell cultures: human prostate cancer androgen-non-responsive DU-145 cells and primary cultures of rat astrocytes.

Observing a column-dependentζin dense interstellar sources: the case of the Horsehead nebula

Context: Observations of small carbon-bearing molecules such as CCH, C4H, c-C3H2, and HCO in the Horsehead Nebula have shown these species to have higher abundances towards the edge of the source than towards the center. Aims: Given the determination of a wide range of values for zeta (s-1), the total ionization rate of hydrogen atoms, and the proposal of a column-dependent zeta(N_H), where N_H is the total column of hydrogen nuclei, we desire to determine if the effects of zeta(N_H) in a single object with spatial variation can be observable. We chose the Horsehead Nebula because of its geometry and high density. Method: We model the Horsehead Nebula as a near edge-on photon dominated region (PDR), using several choices for zeta, both constant and as a function of column. The column-dependent zeta functions are determined by a Monte Carlo model of cosmic ray penetration, using a steep power-law spectrum and accounting for ionization and magnetic field effects. We consider a case with low-metal elemental abundances as well as a sulfur-rich case. Results: We show that use of a column-dependent zeta(N_H) of 5(-15) s-1 at the surface and 7.5(-16) s-1 at Av = 10 on balance improves agreement between measured and theoretical molecular abundances, compared with constant values of zeta.

Quasi-stable neutralinos at the LHC

We study supersymmetric extensions of the Standard Model with small R-parity and lepton number violating couplings which are naturally consistent with primordial nucleosynthesis, thermal leptogenesis and gravitino dark matter. We consider supergravity models where the gravitino is the lightest superparticle followed by a bino-like next-to-lightest superparticle (NLSP). Extending previous work we investigate in detail the sensitivity of LHC experiments to the R-parity breaking parameter zeta for various gluino and squark masses. We perform a simulation of signal and background events for the generic detector DELPHES for which we implement the finite NLSP decay length. We find that for gluino and squark masses accessible at the LHC, values of zeta can be probed which are one to two orders of magnitude smaller than the present upper bound obtained from astrophysics and cosmology.

Q(n) Species Distribution in K2O·2SiO2 Glass by 29Si Magic Angle Flipping NMR

Two-dimensional magic angle flipping (MAF) was employed to measure the Q((n)) distribution in a (29)Si-enriched potassium disilicate glass (K(2)O.2SiO(2)). Relative concentrations of [Q((4))] = 7.2 +/- 0.3%, [Q((3))] = 82.9 +/- 0.1%, and [Q((2))] = 9.8 +/- 0.6% were obtained. Using the thermodynamic model for Q((n)) species disproportionation, these relative concentrations yield an equilibrium constant k(3) = 0.0103 +/- 0.0008, indicating, as expected, that the Q((n)) species distribution is close to binary in the potassium disilicate glass. A Gaussian distribution of isotropic chemical shifts was observed for each Q((n)) species with mean values of -82.74 +/- 0.03, -91.32 +/- 0.01, and -101.67 +/- 0.02 ppm and standard deviations of 3.27 +/- 0.03, 4.19 +/- 0.01, and 5.09 +/- 0.03 ppm for Q((2)), Q((3)), and Q((4)), respectively. Additionally, nuclear shielding anisotropy values of zeta =-85.0 +/- 1.3 ppm, eta = 0.48 +/- 0.02 for Q((2)) and zeta = -74.9 +/- 0.2 ppm, eta = 0.03 +/- 0.01 for Q((3)) were observed in the potassium disilicate glass.

The Arakawa–Kaneko zeta function

We present a very natural generalization of the Arakawa–Kaneko zeta function introduced ten years ago by T. Arakawa and M. Kaneko. We give in particular a new expression of the special values of this function at integral points in terms of modified Bell polynomials. By rewriting Ohno’s sum formula, we are able to deduce a new class of relations between Euler sums and the values of zeta.

Zeta and $L$-functions and Bernoulli polynomials of root systems

This article is essentially an announcement of the papers [7,8,9,10] of the authors, though some of the examples are not included in those papers. We consider what is called zeta and $L$-functions of root systems which can be regarded as a multi-variable version of Witten multiple zeta and $L$-functions. Furthermore, corresponding to these functions, Bernoulli polynomials of root systems are defined. First we state several analytic properties, such as analytic continuation and location of singularities of these functions. Secondly we generalize the Bernoulli polynomials and give some expressions of values of zeta and $L$-functions of root systems in terms of these polynomials. Finally we give some functional relations among them by our previous method. These relations include the known formulas for their special values formulated by Zagier based on Witten’s work.

Functional relations and special values of Mordell-Tornheim triple zeta and 𝐿-functions

In this paper, we prove the existence of meromorphic continuation of certain triple zeta-functions of Lerch’s type. Based on this result, we prove some functional relations for triple zeta and L L -functions of the Mordell-Tornheim type. Using these functional relations, we prove new explicit evaluation formulas for special values of these functions. These can be regarded as triple analogues of known results for double zeta and L L -functions.