On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

A note on robust detection

We introduce a simple new hypothesis testing procedure, which,based on an independent sample drawn from a certain density, detects which of $k$ nominal densities is the true density is closest to, under the total variation (L_{1}) distance. Weobtain a density-free uniform exponential bound for the probability of false detection.

Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Bound state solutions of schrödinger equation for a more general exponential screened coulomb potential via Nikiforov-Uvarov method

The arbitrary angular momentum solutions of the Schrödinger equation for a diatomic molecule with the general exponential screened coulomb potential of the form V(r) = (- a / r){1+ (1+ b )e-2b } has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N2 CO and NO

An exponential lower bound for a restricted class of monotone formulae for 2-unsatisfiability /

"UILU-ENG 78-1734."

The blood volumes of the primary and secondary circulatory system in the Atlantic cod Gadus morhua L., using plasma bound Evans Blue and compartmental analysis

The volume of the primary (PCS) and secondary (SCS) circulatory system in the Atlantic cod Gadus morhua was determined using a modified dye dilution technique. Cod (N=10) were chronically cannulated in the second afferent branchial artery with PE-50 tubing. Evans Blue dye was bound to harvested fish plasma at a concentration of 1 mg dye ml(-1) plasma, and injected at a concentration of 1 mg kg(-1) body mass. Serial sampling from the cannula produced a dye dilution curve, which could be described by a double exponential decay equation. Curve analysis enabled the calculation of the primary circulatory and total distribution volume. The difference between these volumes is assumed to be the volume of the SCS. From the dilution curve, it was also possible to calculate flow rates between and within the systems. The results of these experiments suggest a plasma volume in the PCS of 3.42+/-0.89 ml 100 g(-1) body mass, and in the SCS of 1.68+/-0.35 ml 100 g(-1) body mass (mean +/- S.D.) or approximately 50% that of the PCS. Flow rates to the SCS were calculated as 2.7% of the resting cardiac output. There was an allometric relationship between body mass and blood volumes. Increasing condition factor showed a tendency towards smaller blood volumes of the PCS, expressed as percentage body mass, but this was not evident for the volume of the SCS.

First-passage times for non-Markovian processes: Correlated impacts on bound processes

Our previously developed stochastic trajectory analysis technique has been applied to the calculation of first-passage time statistics of bound processes. Explicit results are obtained for linearly bound processes driven by dichotomous fluctuations having exponential and rectangular temporal distributions.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In vitro selection of RNA molecules that displace cocaine from the membrane-bound nicotinic acetylcholine receptor

The nicotinic acetylcholine receptor (AChR) controls signal transmission between cells in the nervous system. Abused drugs such as cocaine inhibit this receptor. Transient kinetic investigations indicate that inhibitors decrease the channel-opening equilibrium constant [Hess, G. P. & Grewer, C. (1998) Methods Enzymol. 291, 443–473]. Can compounds be found that compete with inhibitors for their binding site but do not change the channel-opening equilibrium? The systematic evolution of RNA ligands by exponential enrichment methodology and the AChR in Torpedo californica electroplax membranes were used to find RNAs that can displace inhibitors from the receptor. The selection of RNA ligands was carried out in two consecutive steps: (i) a gel-shift selection of high-affinity ligands bound to the AChR in the electroplax membrane, and (ii) subsequent use of nitrocellulose filters to which both the membrane-bound receptor and RNAs bind strongly, but from which the desired RNA can be displaced from the receptor by a high-affinity AChR inhibitor, phencyclidine. After nine selection rounds, two classes of RNA molecules that bind to the AChR with nanomolar affinities were isolated and sequenced. Both classes of RNA molecules are displaced by phencyclidine and cocaine from their binding site on the AChR. Class I molecules are potent inhibitors of AChR activity in BC3H1 muscle cells, as determined by using the whole-cell current-recording technique. Class II molecules, although competing with AChR inhibitors, do not affect receptor activity in this assay; such compounds or derivatives may be useful for alleviating the toxicity experienced by millions of addicts.

On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

Metal Ions Bound To The Human Milk Immunoglobulin A: Metalloproteomic Approach.

The presence of calcium, iron, and zinc bound to human milk secretory IgA (sIgA) was investigated. The sIgA components were first separated by two-dimensional polyacrylamide gel electrophoresis and then identified by electrospray ionization-tandem mass spectrometry (ESI MS MS). The metal ions were detected by flame atomic absorption spectrometry after acid mineralization of the spots. The results showed eight protein spots corresponding to the IgA heavy chain constant region. Another spot was identified as the transmembrane secretory component. Calcium was bound to both the transmembrane component and the heavy chain constant region, while zinc was bound to the heavy chain constant region and iron was not bound with the identified proteins. The association of a metal ion with a protein is important for a number of reasons, and therefore, the findings of the present study may lead to a better understanding of the mechanisms of action and of additional roles that sIgA and its components play in human milk.

Self-bound models of compact stars and recent mass-radius measurements

The exact composition of a specific class of compact stars, historically referred to as ""neutron stars,'' is still quite unknown. Possibilities ranging from hadronic to quark degrees of freedom, including self-bound versions of the latter, have been proposed. We specifically address the suitability of strange star models (including pairing interactions) in this work, in the light of new measurements available for four compact stars. The analysis shows that these data might be explained by such an exotic equation of state, actually selecting a small window in parameter space, but still new precise measurements and also further theoretical developments are needed to settle the subject.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.