Related papers: Minimal clones with many majority operations
We shed some new light to the problem of characterizing those functions of several arguments that have a unique identification minor. The 2-set-transitive functions are known to have this property. We describe another class of functions…
In this paper it has been verified, by a computer-based proof, that the smallest size of a complete arc is 14 in PG(2,31) and in PG(2,32). Some examples of such arcs are also described.
In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and…
The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out…
Under the assumption of the minimal model theory for projective klt pairs of dimension $n$, we establish the minimal model theory for lc pairs $(X/Z,\Delta)$ such that the log canonical divisor is relatively log abundant and its restriction…
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
We introduce a new approach to the description of multi-sorted clones (sets of $k$-tuples of operations of the same arity, closed under coordinatewise composition and containing all projection tuples) on a two-element domain. Leveraging the…
In probabilistic cloning with two auxiliary systems, we consider and compare three different protocols for the success probabilities of cloning. We show that, in certain circumstances, it may increase the success probability to add an…
The near-unanimity-closed minions of Boolean functions, i.e., the clonoids whose target algebra contains a near-unanimity function, are completely described. The key concept towards this result is the minorant-minor partial order and its…
Given an infinite set X and an ideal I of subsets of X, the set of all finitary operations on X which map all (powers of) I-small sets to I-small sets is a clone. In a 2001 article, G. Czedli and L. Heindorf asked whether or not for two…
We show that given any two minimal models of a generalized lc pair, there exist small birational models which are connected by a sequence of symmetric flops. We also present some applications.
We will prove the following results for $3$-fold pairs $(X,B)$ over an algebraically closed field $k$ of characteristic $p>5$: log flips exist for $\Q$-factorial dlt pairs $(X,B)$; log minimal models exist for projective klt pairs $(X,B)$…
A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the…
In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.
There are 123,650 partial groups of order at most 9 and 178,937,003 partial groups of order 10. We explain a computer enumeration of these results and provide a complete list of indecomposable partial groups of order at most 5. We also…
Short-length Reed--Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding…
In this paper we obtain at least 61 new singly even (Type I) binary [72,36,12] self-dual codes as a quasi-cyclic codes with m=2 (tailbitting convolutional codes) and at least 13 new doubly even (Type II) binary [72,36,12] self-dual codes by…
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In this paper, we give definitions of three kinds of minimal charts, and we investigate properties of minimal charts and establish fundamental theorems characterizing minimal charts. To classify charts with two or three crossings we use the…
For the computational model where only additions are allowed, the $\Omega(n^2\log n)$ lower bound on operations count with respect to image size $n\times n$ is obtained for two types of the discrete Radon transform implementations: the fast…