This survey gives a concrete and intuitively self-contained introduction to the theory of pure L-functions arising from a family of algebraic varieties defined over a finite field of characteristic p. The standard fundamental questions in any theory of L-functions include the meromorphic continuation, functional equation, Riemann hypothesis (RH for short), order of zeros at special points and t...

We consider the problem of classifying completely unlabeled data by using convex inequalities that contain absolute values of the data. This allows each data point to belong to either one of two classes by entering the inequality with a plus or minus value. By using such absolute value inequalities (AVIs) in support vector machine classifiers, unlabeled data can be successfully partitioned into...

an extended peng-robinson equation of state (epr-eos) is used to model the vapor-liquid equilibrium (vle) in systems containing (water + nacl + co2), (water + methanol + nacl + co2), (water + na2so4 + co2) and (water + nh4cl + co2). the binary and ternary interaction parameters between salt and solvent are adjusted to experimental mean solvent activity of salts (nacl and na2so4). for the system...

The gap equation in the 1 S 0-channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap ∆ turned out to be very sensitive to the cutoff K max in the momentum space in the equation for the effective ...

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-...

A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax−|x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1000-dimensional AVEs to an accuracy of 10−6 in less than 10 seconds each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 10...

This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0. The method of power series leads to a Hermite equation for the generating function of the coefficients which is solved in terms of the parabolic cylinder functions. By integrating out the local time variable, this leads to an integral expression ...

We present a case study of a formal veri cation of a numerical program that computes the discretization of a simple partial di erential equation. Bounding the rounding error was tricky as the usual idea, that is to bound the absolute value of the error at each step, fails. Our idea is to nd out a precise analytical expression that cancels with itself at the next step, and to formally prove the ...

In this paper we consider a guaranteed cost control problem for a class of uncertain discrete-time systems which contain structured uncertainties. The uncertainties are assumed to satisfy a certain sum quadratic constraint. The controller will be a minimax controller in the sense that it minimizes the maximum value of a cost function. For a given initial condition, the minimax optimal controlle...