The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b ∈ Zn, gcd(a− b, n) ∈ D}. Using tools from convex optimization, we study the maxim...

In this paper we study a notion of preorder that arises in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and its generalization to ultrafilters, which is related to the algebraical and topological structure of the Stone-Čech compactification of the discrete space of natural numbers. In particular, we prove that there exist ultrafilters maximal for...

We classify, up to isomorphism, maximal curves covered by the Hermit-ian curve H by a prime degree Galois covering. We also compute the genus of maximal curves obtained by the quotient of H by several automorphisms groups. Finally we discuss the value for the third largest genus that a maximal curve can have.

We focus on L(A), the filter of supersets of A in the structure of the computably enumerable sets under the inclusion relation, where A is an atomless r-maximal set. We answer a long standing question by showing that there are infinitely many pairwise non-isomorphic filters of this type.

‎Here‎, ‎we investigate a conjecture posed by Amiri and Ariannejad claiming‎ ‎that if every maximal subfield of a division ring $D$ has trivial normalizer‎, ‎then $D$ is commutative‎. ‎Using Amitsur classification of‎ ‎finite subgroups of division rings‎, ‎it is essentially shown that if‎ ‎$D$ is finite dimensional over its center then it contains a maximal‎ ‎subfield with non-trivial normalize...

We prove that every tower of normal filters of height δ (δ supercompact) is precipitous assuming that each normal filter in the tower is the club filter restricted to a stationary set. We give an example to show that this assumption is necessary. We also prove that every normal filter can be generically extended to a well-founded V -ultrafilter (assuming large cardinals). In this paper we inves...

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

where u0 = 05 U\ 13 and a and b are integers. We will call a and b the parameters of the recurrence. We will denote such a sequence as u(a3 b) . Two of the most important questions concerning these sequences are: For a given PFLS w(a, 2?), which odd primes have a maximal rank of apparition? and For which odd primes does the PFLS u(a5 b) have a maximal period modulo p? No definitive results are ...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

We present a critical analysis of the maximal prime decomposition of Bayesian networks (BNs). Our analysis suggests that it may be more useful to transform a BN into a hierarchical Markov network.