Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there s...

Let an arbitrarily small positive constant δ less than 1 and a polynomial f with integer coefficients be fixed. We prove unconditionally that f modulo p can be completely factored in deterministic polynomial time if p− 1 has a (ln p)O(1)-smooth divisor exceeding pδ. We also address the issue of factoring f modulo p over finite extensions of the prime field Fp and show that p− 1 can be replaced ...

In the previous paper in ICAT2002, we reported that a non-grounded palm-top torque display "GyroCube" was developed. Although it requires no grounding base for supporting the counter torque to the objective one, and consequently is suitable for mobile use, it generates superfluous negative resetting torque after presenting the objective one in terms of principle. When the control voltage is inc...

Let p be prime and Zpn a degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast deterministic algorithms for common operations in Zpn modulo p . Combining existing methods with recent work of Kedlaya and Umans about modular composition of polynomials, we achieve quasi-linear time algorithms in the parameters n and N , and quasi-linea...

We consider systems of homogeneous linear equations modulo 2 with three variables in each equation and study balanced assignments as solutions to such equations. We prove that it is hard to distinguish systems where there is a balanced assignment that satisfies a fraction 1− ε of the equations from systems where the best balanced assignment satisfies a fraction 2 + ε of the equations assuming t...

Using OECD data (1965-1994) for 22 selected countries; we test for tax burden and per capita GDP convergence based on a time series approach. We further examine the issue of a possible relationship existing between per capita GDP and tax burden convergence. Generally, the evidence from this paper does not show any close relationship between tax burden and per capita GDP convergence.

Let m 6= n. An m × n × p proper array is a three-dimensional array composed of directed cubes that obeys certain constraints. Because of these constraints, the m × n × p proper arrays may be classified via a schema in which each m × n × p proper array is associated with a particular m × n planar face. By representing each connencted component present in the m × n planar face with a distinct let...

Deterministic polynomial time primality criteria for 2n − 1 have been known since the work of Lucas in 1876–1878. Little is known, however, about the existence of deterministic polynomial time primality tests for numbers of the more general form Nn = (p − 1) pn − 1, where p is any fixed prime. When n > (p − 1)/2 we show that it is always possible to produce a Lucas-like deterministic test for t...

Mobile service robots are expected to provide services in various domains of life. Herein, the main challenge for the robot is the execution of complex tasks within an unstructured dynamic environment. In order to achieve the necessary highly flexible behavior, mobile service robots must have a high degree of autonomy. However, although much effort is spent on the investigation and realization ...

In the direct current mode (DC), widely used in electroflocculation (EC), the formation of an impermeable oxide layer on the cathode causes the declining of the efficiency of this process. This disadvantage has been reduced by adopting alternating current (AC). In this study, the effects of AC and DC on operational parameters such as the removal of oils and greases (O&G), color and turbidity fr...