This paper discusses how to improve the Boris pusher used advance relativistic charged particles in fixed electromagnetic fields. We first derive a simple solution flaw previously discovered by others. then new analytic that is minor modification original split-time scheme, except for calculation of γ. assumes change γ during particle small. It less accurate than derived Fei Li et al., but near...

We present a simple, explicit construction of an infinite family F of bounded-degree ’unique-neighbor’ expanders Γ; i.e., there are strictly positive constants α and , such that all Γ = (X,E(Γ)) ∈ F satisfy the following property. For each subset S of X with no more than α|X| vertices, there are at least |S| vertices in X \ S that are adjacent in Γ to exactly one vertex in S. The construction o...

Let Γ=(VΓ,EΓ) be a simple undirected graph with finite vertex set VΓ and edge EΓ. A total n-labeling α:VΓ∪EΓ→{1,2,…,n} is called irregular labeling on Γ if for any two different edges xy x′y′ in EΓ the numbers α(x)+α(xy)+α(y) α(x′)+α(x′y′)+α(y′) are distinct. The smallest positive integer n such that can labeled by irregularity strength of Γ. In this paper, we provide some asymmetric graphs sym...

Let Γ = (V,E) be a simple graph of order n and degree sequence δ1 ≥ δ2 ≥ · · · ≥ δn. For a nonempty set X ⊆ V , and a vertex v ∈ V , δX(v) denotes the number of neighbors v has in X. A nonempty set S ⊆ V is a defensive k-alliance in Γ = (V,E) if δS(v) ≥ δS̄(v) + k, ∀v ∈ S. The defensive k-alliance number of Γ, denoted by ak(Γ), is defined as the minimum cardinality of a defensive k-alliance in Γ...

Abstract Let G be a simple graph with vertex set V (G). A set S ⊆ V (G) is independent if no two vertices from S are adjacent. The graph G is known to be a KönigEgerváry if α (G) + μ (G) = |V (G)|, where α (G) denotes the size of a maximum independent set and μ (G) is the cardinality of a maximum matching. Let Ω(G) denote the family of all maximum independent sets, and f be the function from su...

ABSTRACT Ultrahigh energy protons and nuclei from extragalactic cosmic ray sources initiate intergalactic electromagnetic cascades, resulting in observable fluxes of γ-rays the GeV–TeV domain. The total spectrum such cascade hadronic nature is significantly harder than one usually expected blazars. spectra some known as ‘extreme TeV blazars’ could be well-described by this ‘intergalactic model’...

Abstract. For an (ǫ,Γ)-color-commutative associative algebra A with an identity element over a field F of characteristic not 2, and for a color-commutative subalgebraD of color-derivations of A, denote by A[D] the associative subalgebra of End(A) generated by A (regarding as operators on A via left multiplication) and D. It is easily proved that, as an associative algebra, A[D] is Γgraded simpl...

We introduce a quasiregular analog F of the sine and cosine function such that, for a sufficiently large constant λ, the map x 7→ λF (x) is locally expanding. We show that the dynamics of this map define a representation of Rd, d ≥ 2, as a union of simple curves γ : [0,∞) → Rd which tend to ∞ and whose interiors γ∗ = γ((0,∞)) are disjoint such that the union of all γ∗ has Hausdorff dimension 1.

A finite simple graph Γ is called a Nest if it regular of valency 6 and admits an automorphism ρ with two orbits the same length such that at least one subgraphs induced by these cycle. We say core-free no non-trivial subgroup group generated normal in Aut(Γ). In this paper, we show that, edge-transitive core-free, then isomorphic to following graphs: complement Petersen graph, Hamming H(2,4), ...

We showed in [Oh] that for a simple real Lie group G with real rank at least 2, if a discrete subgroup Γ of G contains lattices in two opposite horospherical subgroups, then Γ must be a non-uniform arithmetic lattice in G, under some additional assumptions on the horospherical subgroups. Somewhat surprisingly, a similar result is true even if we only assume that Γ contains a lattice in one horo...