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### A degree-decreasing lemma for $\left({\text{MOD}}_{q}-{\text{MOD}}_{p}\right)$ circuits.

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

### A Fractional LC − RC Circuit

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05We suggest a fractional differential equation that combines the simple harmonic oscillations of an LC circuit with the discharging of an RC circuit. A series solution is obtained for the suggested fractional differential equation. When the fractional order α = 0, we get the solution for the RC circuit, and when α = 1, we get the solution for the LC circuit. For arbitrary α we get a general solution which shows how the...

### A heuristic algorithm for constructing optimal lookup tables in circuit design.

Southwest Journal of Pure and Applied Mathematics [electronic only]

### A multiplication theorem for two-variable positive real matrices

Aplikace matematiky

A multiplication-division theorem is derived for the positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real functions of two complex variables. The theorem is generalized to encompass the product of positive real matrices whose elements are functions of two complex variables. PRF and PR matrices occur frequantly in the study of electrical multiports and multivariable systems (such as digital filters).

### A theory for ungrounded electrical grids and its application to the geophysical exploration of layered strata

Studia Mathematica

### An algorithm for model reduction in large electric power systems.

Mathematical Problems in Engineering

### Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor.

Mathematical Problems in Engineering

### Controllability, applications, and numerical simulations of cellular neural networks.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Controllability of time-varying cellular neural networks.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Decomposition-based logic synthesis for PAL-based CPLDs

International Journal of Applied Mathematics and Computer Science

The paper presents one concept of decomposition methods dedicated to PAL-based CPLDs. The proposed approach is an alternative to the classical one, which is based on two-level minimization of separate single-output functions. The key idea of the algorithm is to search for free blocks that could be implemented in PAL-based logic blocks containing a limited number of product terms. In order to better exploit the number of product terms, two-stage decomposition and BDD-based decomposition are to be...

### Dynamique des nombres et physique des oscillateurs

Journal de Théorie des Nombres de Bordeaux

Nous présentons un modèle mathématique permettant de reproduire le spectre expérimental des fréquences dans un composant électronique appelé boucle ouverte. Le spectre semble s’organiser suivant une contrainte de nature diophantienne sur les fréquences. Sa structure peut donc se comprendre via une étude de l’ensemble des fractions continues en fonction de leur longueur et de la taille des quotients partiels.

### EKF-based dual synchronization of chaotic colpitts circuit and Chua’s circuit

Kybernetika

In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua’s circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua’s circuit as a higher- dimensional system, while the second method...

### Estimates of topological entropy of continuous maps with applications.

Discrete Dynamics in Nature and Society

### Fully connected PLL networks: how filter determines the number of nodes.

Mathematical Problems in Engineering

### Generalized ternary simulation of sequential circuits

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

### Inductorless Chua's circuit: experimental time series analysis.

Mathematical Problems in Engineering

### Integral representation of $n$-variable positive real functions

Commentationes Mathematicae Universitatis Carolinae

### Invariant resistive networks in Euclidean spaces and their relation to geometry

Aplikace matematiky

Geometric properties of finite systems of homogeneous resistive wire segments in a Euclidean $n$-space are studied in the case that the absorption of energy of such a system in an arbitrary linear electrical field is invariant under any orthogonal transformation of the system.

### Inversion of square matrices in processors with limited calculation abillities

International Journal of Applied Mathematics and Computer Science

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested....