The paper presents a new [pseudo-] Logarithmic Model for Image Processing (LIP), which allows the computation of gray-level addition, substraction and multiplication with scalars within a fixed graylevel range [0;D] without the use of clipping. The implementation of Laplacian edge detection techniques under the proposed model yields superior performance in biomedical applications as compared wi...

Let R be a commutative ring. An R-module M is called co-multiplication provided that foreach submodule N of M there exists an ideal I of R such that N = (0 : I). In this paper weshow that co-multiplication modules are a generalization of strongly duo modules. Uniserialmodules of finite length and hence valuation Artinian rings are some distinguished classes ofco-multiplication rings. In additio...

Let (K,+, ∗) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, ∗) is a skewHadamard difference set or a Paley type partial difference set in (K,+) according as q is congruent to 3modulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter–Matthews presemifield and the Ding–Yuan variation of it, we recover a recent cons...

In a great variety of neuron models, neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units that multiply their inputs instead of summing them and thus allow inputs to interact nonlinearly. The class of multiplicative neural networks comprises such widely known and well-studied network types as higher-order networks ...

Context. The cryptographically secure pseudo-random number generator Blum Blum Shub (BBS) is a simple algorithm with a strong security proof, however it requires very large numbers to be secure, which makes it computationally heavy. The Graphics Processing Unit (GPU) is a common vector processor originally dedicated to computer-game graphics, but has since been adapted to perform general-purpos...

Strong public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF(p) and RSA-1024 and RSA-2048 on two 8-bit microcontrollers. To accelerate multiple-precision multiplication...

BIST (built-in self test) is one of the most attractive solutions to test chips at speed. In this paper, we present a new test pattern generation method using the processing units of DSP (digital signal processing). This method utilizes dual MAC (multiply and accumulate) units, which consist of two multipliers and several accumulators, in DSP to generate test patterns. The proposed test pattern...

A C implementation of Niederreiter’s algorithm for factoring polynomials over F2 is described. The most time-consuming part of this algorithm, which consists of setting up and solving a certain system of linear equations, is performed in parallel. Once a basis for the solution space is found, all irreducible factors of the polynomial can be extracted by suitable gcdcomputations. For this purpos...

There are proven generalizations of the Hölder's and Minkowski's inequalities for the pseudo-integral. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g, the second semiring ([a, b], sup,), where is generated and the third semiring where both pseudo-operations are idempotent, i.e., È = sup an...

We consider Nonlinear Equilibrium (NE) for the optimal allocation of limited resources. The NE is a generalization of Walras-Wald equilibrium, which is equivalent to J. Nash equilibrium in n-person concave games. Finding NE is equivalent to solving a variational inequality (VI) with a monotone and smooth operator on Ω = R+ ⊗ R+ . Projection on Ω is a very simple procedure; therefore, our main f...