We have recently demonstrated' that such a Green's function exists if the polynomial Epl+ -..+pn <2h ap,. ..Pn(itl) PI. .. (itn)P" and both its highest and lowest homogeneous parts occurring, are all three different from zero for any real ti, ..., tn not all zero. THEOREM 1. In En, ifD is a bounded domain having a connected boundary B, and if U is a neighborhood of B, and if an analytic functio...

We define and study a distributed cryptographic implementation for an asynchronous pi calculus. At the source level, we adapt simple type systems designed for establishing formal secrecy properties. We show that those secrecy properties have counterparts in the implementation, not formally but at the level of bitstrings, and with respect to probabilistic polynomial-time active adversaries. We r...

We consider the class of polynomial differential equations ẋ = Pn(x, y)+Pn+1(x, y) +Pn+2(x, y), ẏ = Qn(x, y)+Qn+1(x, y)+Qn+2(x, y), for n ≥ 1 and where Pi and Qi are homogeneous polynomials of degree i. These systems have a linearly zero singular point at the origin if n ≥ 2. Inside this class we identify a new subclass of Darboux integrable systems, and some of them having a degenerate center,...

Problem MQ: Solve the system p1 = p2 = · · · = pm = 0, where each pi is a quadratic polynomial in x = (x1, . . . , xn) and coefficients and variables are in K = GF(q). Generic MQ is NP-hard [GJ79], and consensus pegs it as a difficult problem to solve even probabilistically. The trapdoor is built into the public map P by the knowledge of the maps S and T . The central map Q may contain paramete...

SUMMARY This paper proposes a robust state observer for multi-input multi-output LTI systems. Unknown inputs of polynomial form and high-frequency measurement noises are considered in the system model. The unknown inputs and the noises are not in the same form. Multiple integra-tions of both the observer error signal and the measurement output are used for the observer design. The existence con...

The problem. We study a new geometric optimization problem which arises in carrot crop management [10], as well as wireless network design and various other facililty location problems. The task is to select a number of locations t j for the sprinklers, and assign a radius r j to each sprinkler. A carrot pi is covered iff it is within range of some transmission point t ji , i.e., d(t ji , pi) ≤...

Abstract: The association between beneficial microorganisms and green beans can accelerate establishment in the field. objective of this study was to investigate influence seed treatments different doses Bacillus subtilis on physiological potential beans. Seeds from cultivar Macarrão Baixo were used. used a completely randomized design double factorial scheme with factor A treatments: Pellicula...

safflower is one of the oldest cultivated plants and oilseed as a native iran could have in the development of oilseeds cultivation. to evaluate the morphological characteristics of safflower (carthamus tinctorius l) an experiment was conducted as a completely randomized design. the figures include 1- pi 23755 2-pi 239041 3- pi 250202 4- pi 250532 5- pi 25268 6- pi 253515 7- pi 253541 8- pi 253...

Investigated in this paper are the uniform approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by an SOPNN with its activation function in C(R) is dense in C(K) for any compact K ∈ R , if and only if the activation function is not a polynomial. It is also shown that if the activation function ...

Let K be a number field and p be a prime number. When we factor (p) = pOK into prime ideals, say (p) = p1 1 · · · p eg g , we refer to the data of the ei’s, the exponents fi in the norms Npi = p fi , and g (the number of pi’s), as the “shape” of the factorization of (p). (What we are leaving out of this is explicit information about generators for the ideals pi.) Similarly, if a monic polynomia...