We study the existence of weak solutions to (E) (−∆)u+g(u) = ν in a bounded regular domain Ω in R (N ≥ 2) which vanish in R \Ω, where (−∆) denotes the fractional Laplacian with α ∈ (0, 1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of a weak solution for pr...

Here, gyroscopic systems are time-invariant systems for which motions can be characterized by properties of a matrix pencil L(λ) = λ2I + λG − C, where GT = −G and C > 0. A strong stability condition is known which depends only on |G| (= (GT G)1/2 ≥ 0) and C. If a system with coefficients G0 and C satisfies this condition then all systems with the same C and with a G satisfying |G| ≥ |G0| are al...

In this paper, we introduce the notion of strictly (α,ψ,ξ)-G-contractive mappings in b-metric spaces endowed with a graph G. We establish a sufficient condition for existence and uniqueness of points of coincidence and common fixed points for such mappings. Our results extend and unify many existing results in the literature. Finally, we construct some examples to analyze and support our results.

Two graphs G and H are called R-cospectral if A(G)+yJ and A(H)+yJ (where A(G), A(H) are the adjacency matrices of G and H, respectively, J is the all-one matrix) have the same spectrum for all y ∈ R. In this note, we give a necessary condition for having R-cospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal similarity between certain cospectral grap...

The G-rich strand of human telomeric DNA can fold into a four-stranded structure called G-quadruplex and inhibit telomerase activity that is expressed in 85-90% tumor cells. For this reason, telomere quadruplex is emerging as a potential therapeutic target for cancer. Information on the structure of the quadruplex in the physiological environment is important for structure-based drug design tar...

For any Lie algebra g we introduce the notion of g symplectic structures and show that every orbit of a principal G bundle carries a natural g symplectic form and an associated momentum map induced by the Maurer Cartan form on G . We apply this to the BRST bicomplex and show that the associated momentum map is a solution of the Wess-Zumino consistency condition for the anomaly. Research partial...

in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

Let G be a generalized dicyclic group with identity 1. An inverse closed subset S of G∖{1} is called minimal if 〈S〉=G and there exists some s∈S such that 〈S∖{s,s−1}〉≠G. In this paper, we characterize distance-regular Cayley graphs Cay(G,S) under the condition minimal.

Theorem 1 Let G = (V, E) be a plane graph and let H = (T, R) be a demand graph where T is the set of vertices of a single face of G. Then if G satisfies the cut condition for H and G + H is eulerian, there is an integral multiflow for H in G. The proof is via induction on 2|E| − |R|. Note that if G satisfies the cut condition for H, then |R| ≤ |E| (why?). There are several " standard " inductio...

a r t i c l e i n f o a b s t r a c t Keywords: Valuation independence Generalized series fields Fields of Puiseux series Restricted exponential function We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K , we give a sufficient condition for a valued subfield of the field of gene...