Let A be a nite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to nd lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse problem for subset sums is to determine the structure of the extremal sets A of integers for which jS h ...

Recent advances in the technology of transmission electron microscopy have allowed for a more precise visualization of materials and physical processes, such as metal oxidation. Nevertheless, the quality of information is limited by the damage caused by an electron beam, movement of the specimen or other environmental factors. A novel registration method has been proposed to remove those limita...

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

We obtain the general k-correlations for a short divisor sum related to primes.

Any weighted automaton (WA) defines a relation from finite words to values: given an input word, its set of values is obtained as the set of values computed by each accepting run on that word. A WA is k-valued if the relation it defines has degree at most k, i.e., every set of values associated with an input word has cardinality at most k. We investigate the class of quantitative languages defi...

– Channel simulators based on Rice’s sum-of-sinusoids are playing an important role in mobile fading channel modelling. However, the parameters of the sum-of-sinusoids have to be determined sophisticated to fully exploit the great potential that this powerful procedure has to offer. This paper provides a fundamental work on the stationary and ergodic properties of sum-of-sinusoids-based Rayleig...

In this paper we present an one-and-a-half-line proof, involving Cogalois Theory, of a folklore result asking when is an irrational number a sum of radicals of positive rational numbers. Some of the main ingredients of Cogalois Theory like G-Kneser extension, G-Cogalois extension, etc., used in the proof are briefly explained, so that the paper is selfcontained. We also discuss some older and n...

A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let D k (G) denote the smallest ℓ such that each sequence over G of length at least ℓ has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (D k (G)) ...

We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov–Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field this derivation also extends the known nonequilibrium moment sum rules for the Green functions to the third moment . These sum rules are used to further test the accuracy of no...