We prove a convergence result for family of Yang–Mills connections over an elliptic $K3$ surface $M$ as the fibers collapse. In particular, assume is projective, admits section, and has singular Kodaira type $I_1$ $II$. Let $\Xi_{t_k}$ be sequence $SU(n)$ on principal bundle $M$, that are anti-self-dual with respect to Ricci flat metrics collapsing $M$. Given certain non-degeneracy assumptions ...

A {\em theta} is a graph made of three internally vertex-disjoint chordless paths $P_1 = \dots b$, $P_2 $P_3 b$ length at least~2 and such that no edges exist between the except incident to $a$ $b$. pyramid} b_1$, b_2$, b_3$ least~1, two which have least 2, $a$, $b_1b_2b_3$ triangle those to~$a$. An \emph{even hole} cycle even length. For non-negative integers $i\leq j\leq k$, let $S_{i,j,k}$ b...

Abstract We consider the following problem: for a given graph G and two integers k d , can we apply fixed operation at most times in order to reduce parameter $$\pi $$ π by least ? show that this problem is NP-hard when independence number vertex deletion or edge contraction, even $$d=1$$ d...

Four stars pulsating simultaneously with a dominant period $P_D$$\in$(0.28,0.39) d and an {\it additional} $P_A$$\in$(0.20,0.27) have been identified from among the more than 3000 RR Lyrae observed by Kepler space telescope during NASA's K2 Mission. All four are located in direction of Galactic Bulge ratios, $P_A$/$P_D$, significantly smaller those most double-mode (RRd) stars: $P_A$/$P_D$$\in$...

We analyze the quasi-two-body charmed $B$ decays $B^{+,0}_{(s)} \to D_{(s)}^* P_2 D_{(s)} P_1 P_2$ with $P_{1,2}$ as a pion or kaon. The intermediate processes $B_{(s)} $ are calculated factorization-assisted topological-amplitude approach and resonant effects Breit-Wigner formalism. Taking all p-wave resonance states \bar D_{(s)}^*$ into consideration, we present related branching fractions, c...

As part of an All-Sky Automated Survey for SuperNovae (ASAS-SN) search sources with large flux decrements, we discovered a transient where the quiescent, stellar source, ASASSN-V J192114.84+624950.8, rapidly decreased in by $\sim55\%$ ($\sim0.9$ mag) g-band. The \textit{TESS} light curve revealed that source is highly eccentric, eclipsing binary. Fits to using \textsc{phoebe} find binary orbit ...

Very few results are known which yield the crossing number of an infinite class of graphs on some surface. In this paper it is shown that by taking the class of graphs to be ¿-dimensional cubes Q(d) and by allowing the genus of the surface to vary, we obtain upper and lower bounds on the crossing numbers which are independent of d. Specifically, if the genus of the surface is always y(Q(d))—k, ...

Abstract Kim and Vu made the following conjecture ( Advances in Mathematics , 2004): if $$d\gg \log n$$ d≫logn then random d -regular graph $${\mathscr {G}}(n,d)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">G<...

Consider the generalized absolute value function defined by $$a(t) = \left| t \right|{t^{n - 1}},\,\,\,\,\,t \in \mathbb{R},n {\mathbb{N}_{\ge 1}}.$$ . Further, consider n-th order divided difference a[n]: ℝn+1 → ℂ and let 1 < p1, …, pn ∞ be such that $$\sum\nolimits_{l 1}^n {p_l^{- 1} $$ Let $${{\cal S}_{{p_l}}}$$ denote Schatten-von Neumann ideals S}_{1,\infty}}$$ weak trace class ideal. We s...