We prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into n-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and p-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists...

New data are presented on the phase equilibria and crystal chemistry of the binary systems CaO-Bi2O3 and CaO-CuO and the ternary CaO-Bi2O3-CuO. Symmetry data and unit cell dimensions based on single crystal and powder x-ray diffraction measurements are reported for several of the binary CaO-Bi2O3 phases, including corrected compositions for Ca4Bi6O13 and Ca2Bi2O5. The ternary system contains no...

An NMOS circuit realization is proposed for ternary functions based on a digital summation threshold gate. The procedure is systematic and any ternary function can be realized with a single gate. Many ternary functions were realized and the resulting circuits were simulated using the MCNC ( Microelectronics Center for North Carolina ) tools for VLSI design. The speed and complexity of the gate ...

We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Principles of weak negation are shown to be isolable, thus defining a number of subminimal negations in the B+ context. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending t...

We review the main difficulties and advantages in developing CMOS ternary circuits. In addition to employing multiple power sources and multiple thresholds, we describe a new theory of transmission functions for designing CMOS ternary logic circuits. It can explain the main CMOS ternary circuits proposed previously. Computer simulations show that the circuits based on the transmission-function ...

The Hausdorff–Alexandroff Theorem states that any compact metric space is the continuous image of Cantor’s ternary set C. It is well known that there are compact Hausdorff spaces of cardinality equal to that of C that are not continuous images of Cantor’s ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of C. Here we present a compact counta...

Wireless Sensor Networks are increasing their capacity to handle larger amounts of data. These networks, which were born with the purpose of collecting environmental information, could be also used for wideband applications, e.g. transmitting audio and / or video data streams. The European project EAR-IT [1] uses acoustic detection to make smarter cities. The idea is to make large-scale deploym...

We study a construction of the Mathieu group M12 using a game reminiscent of Loyd’s “15-puzzle”. The elements of M12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a “pseudogroup” M13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, a...

The goal of this paper is to introduce the description logic ALCRP(D). This logic is based on the DL ALCRP(D) extended by a ternary role-forming predicate operator and by inverse roles. In order to be able to define a compositional semantics for ALCRP(D), which supports n-ary relations, we introduce a DLR-style syntax. For simplicity and from the viewpoint of the applicability in practice, only...